NAME ______DATE ______PERIOD ______

Lesson 1

Area of

Words The area A of a is the product of any base b and its height h.

Symbols A = bh Model

Example 1 Find the area of the parallelogram. A = bh Area of parallelogram A = 4 × 7 Replace b with 4 and h with 7. A = 28 Multiply. The area is 28 units or 28 units2.

The base is 4 units, and the height is 7 units.

Example 2 Find the height of the parallelogram. A = bh Area of parallelogram

24 = 6 ꞏ h Replace A with 24 and b with 6. Divide each side by 6. 4 = h Simplify. So, the height is 4 inches.

Find the area of each parallelogram. 1. 2. 3.

4. Find the height of a parallelogram if its base is 9 feet and its area is 27 square feet.

NAME ______DATE ______PERIOD ______. Lesson 1 Skills Practice

Area of Parallelograms

Find the area of each parallelogram. 1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

13. Find the base of a parallelogram with an area of 18 square inches and a height of 2 inches.

14. Find the height of a parallelogram with an area of 63 square yards and base 9 yards.

15. Find the height of a parallelogram with an area of 41 square meters and base 8.2 meters.

NAME ______DATE ______PERIOD ______

Lesson 2

Area of

Words The area A of a is one half the product of any base b and its height h. Symbols A = bh or A = Model

Examples 1. Find the area. 2. Find the height.

A = Area of a triangle The measure of the 42 = Replace A with 42 and b with 14. base is 5 units, and the height is 8 units. 42(2) = (2) Multiply both sides by 2. A = Area of a triangle 84 = 14 • h Simplify. A = Replace b with 5 and h with 8. Divide by 14. A = Simplify the numerator. 6 = h Simplify. A = 20 Divide. The area is 20 square units. The height is 6 meters.

Exercises Find the area of each triangle. 1. 2. 3.

Find the missing dimension.

4. height: 12 in., area: 24 in2 5. base: 15 m, area: 37.5 m2

NAME ______DATE ______PERIOD ______

Lesson 2 Skills Practice

Area of Triangles

Find the area of each triangle. 1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11. 12.

Find the missing dimension.

13. base: 4 in. 14. height: 1 yd 15. base: 5 ft area: 22 in2 area: 2.5 yd2 area: 5 ft2

NAME ______DATE ______PERIOD ______

Lesson 3

Area of Trapezoids

A trapezoid has two bases, b1 and b2. The height of a trapezoid is the distance between the two bases. The area A of a trapezoid equals half the product of the height h and the sum of the bases b1 and b2. 𝐴 ℎ𝑏 𝑏

Example Find the area of the trapezoid.

A = h(b1 + b2) Area of a trapezoid A = (4)(3 + 6) Replace h with 4, b1 with 3, and b2 with 6. A = (4)(9) Add 3 and 6. A = 18 Simplify.

The area of the trapezoid is 18 square centimeters.

Exercises Find the area of each figure. Round to the nearest tenth if necessary.

1. 2.

3. 4.

NAME ______DATE ______PERIOD ______

Lesson 3 Skills Practice

Area of Trapezoids

Find the area of each figure. Round to the nearest tenth if necessary.

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

11. trapezoid: bases 22.8 mm and 19.7 mm, height 36 mm

12. trapezoid: bases 5 ft and 3.5 ft, height 7 ft

13. DESKS What is the area of the top of the desk shown at right?

NAME ______DATE ______PERIOD ______

Lesson 4

Polygons on the Coordinate Plane

You can use coordinates of a figure to find its dimensions by finding the distance between two points. To find the distance between two points with the same x-coordinates, subtract their y-coordinates. To find the distance between two points with the same y-coordinates, subtract their x-coordinates.

Example A has vertices A(1,1), B(1,3), C(5,3), and D(5,1). Use the coordinates to find the length of each side. Then find the perimeter of the rectangle. Width: Find the length of the horizontal lines. 𝐴𝐷 is 4 units long.

𝐵𝐶 is 4 units long. Length: Find the length of the vertical lines. 𝐴𝐵 is 2 units long. 𝐷𝐶 is 2 units long. Add the lengths of each side to find the perimeter. 4 + 4 + 2 + 2 = 12 units So, rectangle ABCD has a perimeter of 12 units.

Exercises Use the coordinates to find the length of each side of the rectangle. Then find the perimeter.

1. R(1,1), S(1,7), T(5,7), U(5,1) 2. E(3,6), F(7,6), G(7,2), H(3,2)

NAME ______DATE ______PERIOD ______

Lesson 4 Skills Practice

Polygons on the Coordinate Plane

Use the coordinates to find the length of each side of the rectangle. Then find the perimeter.

1. E(1,7), F(3,7), G(3,4), H(1,4) 2. W(2,7), X(2,0), Y(6,0), Z(6,7)

Find the area of each figure in square units.

3. 4.

5. 6.

NAME ______DATE ______PERIOD ______

Lesson 5

Area of Composite Figures

To find the area of a composite figure, separate it into figures whose areas you know how to find, and then add the areas.

Example Find the area of the figure at the right in square feet. The figure can be separated into a rectangle and a trapezoid. Find the area of each.

Area of Rectangle

A = ℓw Area of a rectangle. A = 12 • 8 Replace ℓ with 12 and w with 8. A = 96 Multiply.

Area of Trapezoid A = h(b1 + b2) Area of a trapezoid A = (4)(4 + 12) Replace h with 4, b1 with 4, and b2 with 12. A = 32 Multiply. The area of the figure is 96 + 32 or 128 square feet.

Exercises Find the area of each figure. Round to the nearest tenth if necessary.

1. 2.

3.

NAME ______DATE ______PERIOD ______

Lesson 5 Skills Practice

Area of Composite Figures

Find the area of each figure. Round to the nearest tenth if necessary.

1. 2.

3. 4.

5. 6.

7. 8.

NAME ______DATE ______PERIOD ______

Lesson 6

Volume of Rectangular Prisms

The amount of space inside a three-dimensional figure is the volume of the figure. Volume is measured in cubic units. This tells you the number of of a given size it will take to fill the .

The volume V of a rectangular prism is the product of its You can also multiply the area of the base B by the height length ℓ, width w, and height h. h to find the volume V. Symbols V = ℓwh Symbols V = Bh Model Model

Example Find the volume of the rectangular prism. Method 1 Use V = ℓwh. Method 2 Use V = Bh. V = ℓwh V = Bh V = 10 × 5 × 2 V = 50 × 2 V = 100 V = 100 The volume is 100 ft3. The volume is 100 ft3.

Exercises Find the volume of each prism. 1. 2.

3. 4.

NAME ______DATE ______PERIOD ______

Lesson 6 Skills Practice

Volume of Rectangular Prisms

Find the volume of each prism.

1. 2. 3.

4. 5. 6.

7. 8. 9.

Find the missing dimension of each prism.

10. 11. 12.

13. Find the volume of a rectangular prism with length 9 meters, width 4 meters, and height 5 meters.

14. What is the volume of a rectangular prism with length 6 yards, width 3 yards, and a height of 2 yards?

NAME ______DATE ______PERIOD ______

Lesson 7

Volume of Triangular Prisms

Volume of a Triangular Prism Model Words The volume V of a triangular prism is the area of the base B times the height h.

Symbols V = Bh, where B = bh

Example 1 Find the volume of the triangular prism. The area of the triangle is • 4.5, so replace B with • 4 • 5. V = Bh Volume of a prism

V = ∙ 4 ∙ 5(h) Replace B with ꞏ 4 ꞏ 5. V = ∙ 4 ∙ 5(8) Replace h with 8, the height of the prism. V = 80 Multiply. The volume is 80 cubic inches or 80 in3.

Example 2 Find the volume of the triangular prism. V = Bh Volume of a prism V = ∙ 7 ∙ 10 (h) Replace B with • 7 • 10. V = ∙ 7 ∙ 10 (6) Replace h with 6, the height of the prism. V = 210 Multiply.

The volume is 210 cubic centimeters or 210 cm3.

Exercises Find the volume of each prism. Round to the nearest tenth if necessary.

1. 2. 3.

NAME ______DATE ______PERIOD ______

Lesson 7 Skills Practice

Volume of Triangular Prisms

Find the volume of each prism. Round to the nearest tenth if necessary.

1. 2. 3.

4. 5. 6.

7. 8. 9.

NAME ______DATE ______PERIOD ______

Lesson 8

Surface Area of Rectangular Prisms

The S.A. of a rectangular prism with length ℓ, width w, and height h is the sum of the areas of the faces. Model Symbols S.A. = 2ℓh + 2ℓw + 2hw

Example Find the surface area of the rectangular prism. Find the area of each face. front and back 2ℓh = 2(8)(3) = 48 top and bottom 2ℓw = 2(8)(5) = 80 two sides 2hw = 2(3)(5) = 30

Add to find the surface area. The surface area is 48 + 80 + 30 or 158 square meters.

Exercises Find the surface area of each rectangular prism.

1. 2. 3.

4. 5. 6.

NAME ______DATE ______PERIOD ______

Lesson 8 Skills Practice

Surface Area of Rectangular Prisms

Find the surface area of each rectangular prism.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. Find the surface area of a rectangular prism that is 3 feet by 4 feet by 6 feet.

11. What is the surface area of a rectangular prism that measures 12 meters by 11 meters by 9 meters?

NAME ______DATE ______PERIOD ______

Lesson 9

Surface Area of Triangular Prisms

Model Words

The surface area of the triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces.

Example 1 Find the surface area of the triangular prism. To find the surface area of the triangular prism, find the area of each face and add. area of each triangular base: (12)(10.4) = 62.4 area of each rectangular face: 12(20) = 240 Add to find the surface area. 62.4 + 62.4 + 240 + 240 + 240 = 1,084.8 square centimeters

Example 2 Find the surface area of the triangular prism. Find the area of each face and add. For this prism, each rectangular face has a different area. area of each triangular base: (12)(5) = 30 area of the rectangular faces: 12(10) = 120 5(10) = 50 13(10) = 130

Add to find the surface area. 30 + 30 + 120 + 50 + 130 = 360 square yards

Exercises Find the surface area of each triangular prism.

1. 2.

NAME ______DATE ______PERIOD ______

Lesson 9 Skills Practice

Surface Area of Triangular Prisms

Find the surface area of each triangular prism. Round to the nearest tenth if necessary.

1. 2.

3. 4.

5. 6.

7. A box of snack crackers is in the shape of a triangular prism. What is the surface area of the box?

NAME ______DATE ______PERIOD ______

Lesson 10

Surface Area of Pyramids

Model Words The surface area of a pyramid is the sum of the area of the base and the areas of the lateral faces.

Example 1 Find the surface area of the pyramid. Use a net to find the area of each face and then add. area of the base: 5(5) = 25 area of each triangular side: (5)(7) = 17.5 Add to find the surface area. 25 + 17.5 + 17.5 + 17.5 + 17.5 = 95 square centimeters

Example 2 Find the surface area of the pyramid. Find the area of each face and then add. The triangular base is an because all three sides are 8 feet long. area of the base: (8)(6.9) = 27.6 area of each lateral face: (8)(9) = 36 Add to find the surface area.

27.6 + 36 + 36 + 36 = 135.6 square feet

Exercises Simplify each expression. Justify each step.

1. 2.

NAME ______DATE ______PERIOD ______

Lesson 10 Skills Practice

Surface Area of Pyramids

Find the surface area of each pyramid. Round to the nearest tenth if necessary.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. OFFICE DÉCOR Mr.Statsko has a paper weight on his desk in the shape of a square pyramid. The dimensions of the pyramid are shown. What is the surface area of the paper weight?

NAME ______DATE ______PERIOD ______Answer Key

Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5

Area of Area of Triangles Area of Polygons on the Area of Parallelograms Trapezoids Coordinate Composite Plane Figures 1. 8 units2 1. 10 units2 1. 52.5 in2 1. 20 units 1. 65 cm2 2. 630 cm2 2. 5 ft2 2. 175.5 cm2 2. 16 units 2. 15 in2 3. 91.52 m2 3. 92.4375 in2 3. 198 in2 3. 120 in2 4. 3 ft 4. 4 in 4. 0.5 m2 5. 5 m Skills Practice (Even Numbers Only)

2. 18 units2 2. 15 units2 2. 4.5 ft2 2. 22 units 2. 66 mm2 4. 63 yd2 4. 24 ft2 4. 19 ft2 4. 24 square 4. 55.5 cm2 6. 90 yd2 6. 37.5 in2 6. 331.2 mm2 units 6. 234 yd2 8. 158.8125 in2 8. 9 cm2 8. 30.4 in2 6. 33 square 8. 91 ft2 10. 68.85 cm2 10. 90 m2 10. 136.2 mm2 units 12. 255 m2 12. 98 ft2 12. 29.8 ft2 14. 7 yd 14. 5 yd

Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10

Volume of Volume of Surface Area of Surface Area of Surface Area of Rectangular Triangular Prisms Rectangular Triangular Prisms Pyramids Prisms Prisms 1. 24 ft3 1. 168 ft3 1. 24 in2 1. 920 ft2 1. 896 in2 2. 64 in3 2. 360 in3 2. 34 cm2 2. 57.4 m2 2. 17.4 m2 3. 500 yd3 3. 70 m3 3. 160 ft2 4. 32.832 cm3 4. 54 m2 5. 303.75 in2 6. 122.1 yd3

Skills Practice (Even Numbers Only)

2. 56 m3 2. 86.4 m3 2. 136 ft2 2. 1,176 km2 2. 152 ft2 4. 40 mm3 4. 288 m3 4. 40 yd2 4. 811.2 m2 4. 161.2 cm2 6. 1,800 yd3 6. 758.8 in3 6. 124 ft2 6. 4,802.4 mm2 6. 331.2 mm2 8. 200 ft3 8. 347.5 cm3 8. 176.75 in2 8. 174 ft2 10. 4.7 m 10. 108 ft2 10. 84 in2 12. 3 yd 14. 36 yd3

NAME ______DATE ______PERIOD ______

Geometry Unit Quiz

Find the area of each figure.

1.

1.______

2.

2. ______

3.

3. ______

4.

4. ______

5.

5. ______

6. Find the height of a parallelogram with an area of 224 square meters and a base of 16 meters. 6. ______

7. Find the height of a triangle with an area of 245 square inches and a base of 14 inches. 7. ______

8. Find the height of a parallelogram with an area of 300 square yards and a base of 15 yards. 8. ______

NAME ______DATE ______PERIOD ______

Find the volume of each prism. Round to the nearest tenth if necessary.

9.

9. ______

10.

10. ______

11.

11. ______

12.

12. ______

13. RECREATION The triangular base of a skateboard ramp has an area of 2.3 square meters. The height of the ramp is 1.2 meters. Find the volume of the triangular prism. 13. ______

14. Find the missing dimension of a rectangular prism with a volume of 120 cubic feet, a width of 4 feet, and a length of 4 feet. 14. ______

15. A rectangular prism has a volume of 2,288 cubic meters, a height of 13 meters, and a length of 22 meters. What is the measure of the missing 15. ______dimension?