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Perimeter, Area, and Volume

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Perimeter, Area, and Volume Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the distance in feet, yards, or meters. In math, we usually measure the perimeter of polygons. To find the perimeter of any polygon, we add the lengths of the sides. 2 m 2 m P = 2 m + 2 m + 2 m = 6 m 2 m 3 ft. 1 ft. 1 ft. P = 1 ft. + 1 ft. + 3 ft. + 3 ft. = 8 ft. 3ft When we measure perimeter, we always use units of length. For example, in the triangle above, the unit of length is meters. For the rectangle above, the unit of length is feet. PRACTICE! 1. What is the perimeter of this figure? 5 cm 3.5 cm 3.5 cm 2 cm 2. What is the perimeter of this figure? 2 cm Area Perimeter, Area, and Volume Remember that area is the number of square units that are needed to cover a surface. Think of a backyard enclosed with a fence. To build the fence, we need to know the perimeter. If we want to grow grass in the backyard, we need to know the area so that we can buy enough grass seed to cover the surface of yard. The yard is measured in square feet. All area is measured in square units. The figure below represents the backyard. 25 ft. The area of a square Finding the area of a square: is found by multiplying side x side. 1. Estimate: s x s 20 x 20 = 400+ sq. ft. 25 ft. Area = side x side 2. Calculate: s x s 25 x 25 = 625 sq. ft. To find the area of a rectangle, we can simply multiply the length by the width. Example: If we needed to determine how much paint to buy to paint a wall in this classroom, we would have to figure out how many square feet were on the wall. When we measure the wall, we find that it is 12 feet across and 8 feet high. We can use a piece of graph paper to lay out a model of the wall. 12 ft. 8 ft. Area of Rectangle = l x w How many square feet are on that classroom wall? PRACTICE! 1. Find the perimeter and area of your desk. 2. Use a piece of graph paper to lay out a model of your desk. Area of a Right Triangle Perimeter, Area, and Volume Finding the area of a right triangle might be a little more challenging. The right triangle has two sides that we call the Height and the Base. The dashed lines in the Height diagram show us that a right triangle is simply half of the rectangle that we make if we flip the triangle Base along its third side. Right Angle To find the area of the right triangle, we multiply the base by the height and then divide by 2. We divide by 2 because the triangle is half the rectangle. When we multiply base times height, it is the same as multiplying length by width. Area = Base x Height 2 The area of the right triangle in the grid below would be: A = 5 x 6 2 6 in (Height) A = 30 2 A = 15 inches 5 in (Base) 1 We may also see this formula written as: Base x Height. 2 PRACTICE! 1. Find the area of the right triangle. 4 cm 2 cm Volume Perimeter, Area, and Volume Volume is a measure of capacity or space. Capacity is the space inside a solid figure. For example, think of a rectangular box (which is really a rectangular prism) that is measured in centimeters. Its volume is the number of centimeter cubes that will fit inside the box. Cubic centimeters are represented by this symbol: cm3 We buy dirt, sand, and other outdoor materials in cubic units such as cubic feet, cubic yards, and cubic meters. To find the volume of a rectangular solid, we multiply length x width x height. The formula for finding the Volume of a Rectangular Solid is l x w x h. 3ft 2ft 5ft V = l x w x h V = 3 ft x 2 ft x 5 ft V = 30 ft3 or cubic feet Many cardboard boxes are labeled with their capacity, or amount of space inside, so that we will know how much they will hold. PRACTICE! 1. Find the area of the rectangular prism below. 2 cm 1 cm 3 cm PRACTICE! Perimeter, Area, and Volume 1. Which of the following would require finding the perimeter of something? Buying enough picture frame material to go around my school picture Buying enough sand to fill my little sister’s sandbox Buying enough paint to cover my bedroom wall Buying enough fencing to go around the playground 2. Which of the following would require finding the area of something? Buying enough picture frame material to go around my school picture Buying enough sand to fill my little sister’s sandbox Buying enough paint to cover my bedroom wall Buying enough fencing to go around the playground 3. Which of the following would require finding the volume of something? Buying enough picture frame material to go around my school picture Buying enough sand to fill my little sister’s sandbox Buying enough paint to cover my bedroom wall Buying enough fencing to go around the playground 4. Try these practice problems! Remember to identify the units! Description: Perimeter Area Volume Square: s = 3 cm Rectangle: l = 6 m w = 3 m Triangle: b = 5 in h= 4 in Rectangular Solid l = 2m w = 1m h = 4 m .
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