"Altitude Worksheets - DOC"
-6- Areas of Geometric Shapes Areas of Triangles We can use what we know about finding the area of rectangles to find the area of triangles. We will see that we can change any triangle into a rectangle. Watch how we do this. Start with a triangle like this one. Make an exact copy so there are two of them. We want to make a rectangle from these two triangles. Draw the height of one of the triangles. Cut out this whole triangle and cut along the height. You now have the original triangle and two new right triangles. Move the right triangles so their slanted sides match-up with the slanted sides of the original triangle and the whole shape turns out to be a rectangle. Do Areas of Triangles Worksheet 1 now. -7- By doing Worksheet 1 you now know how to find the area of a triangle. Rule: To find the area of a triangle, multiply the base times the altitude and then take one-half . Written as a formula it is: A = ½ bh Where A stands for the area, b for the base, and h for the height. Even though the ½ comes first, multiply the base and height first and then take one-half. Read the examples below. They show how to find the area of a triangle. Example 1: For a triangle with a base of 9 inches and an altitude of 4 inches, First multiply 9 times 4 to get 36 Then take one-half of 36 to get 18 The area of the triangle is 18 square inches You can write the answer as 18 square inches or 18 sq in or 18 in2 Example 2: For a triangle with a base of 3.7 inches and an altitude of 2.5 inches First multiply 3.7 times 2.5 to get 9.25 (use a calculator) Then take one-half of 9.25 to get 4.625 (use a calculator) The area of the triangle is 4.625 sq in or 4.625 in2 Notice the area answer is given as square inches. Remember when you find area you are trying to determine how many one-inch squares are inside the triangle. Do worksheet 2 now. -8- Areas of Geometric Shapes Areas of Triangles Worksheet 1 For this worksheet we will take two triangles and turn them into a rectangle. Both triangles are exactly the same so they have the same area. Read all the directions before you start to cut. Directions: 1. Draw the height of the bottom triangle. 2. Cut out the bottom triangle and cut along the height to get two right triangles. 3. Match the slanted sides of the two right triangles with the slanted sides of the top triangle to make a rectangle. -9- Areas of Geometric Shapes Areas of Triangles Worksheet 1 Cont. Questions: 1. How much larger is the area of the rectangle than the area of one of the original triangles? Explain why. 2. How does the length of the base of the original triangle and the length of the base of the rectangle compare? 3. How does the length of the height of the original triangle and the length of the height of the rectangle compare? 4. Since the area of the rectangle is the base times the height, A = bh, what is the area of the triangle? Write a formula for this. - 10 - Areas of Geometric Shapes Areas of Triangles Worksheet 2 The area of a triangle is found by multiplying the base times the altitude and then taking one-half. Remember that height is another word for altitude. The formula for finding the area of a triangle is: A = ½ bh A stands for area, b for base and h for height. 1. A triangle has a base of 7 inches and an altitude of 9 inches. Find its area. 2. A triangle has a base of 6 ¾ inches and an altitude of 4 ¼ inches. Find its area. 3. Find the area of the triangles below. 15 inches 9 inches 8 inches 18 inches Area = _________________ 4. 5 inches 3 inches 4 inches Area = _________________