NAME _____________________________________________ DATE ____________________________ PERIOD _____________ Lesson 1 Area of Parallelograms Words The area A of a parallelogram 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 square 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 Triangles Words The area A of a triangle 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. 2 2 4. height: 12 in., area: 24 in 5. base: 15 m, area: 37.5 m 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. ℎ 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 rectangle 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. is 4 units long. is 4 units long. Length: Find the length of the vertical lines. is 2 units long. 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 cubes of a given size it will take to fill the prism. 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 surface area 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.