Answer:
57.74 yd²
Step-by-step explanation:
First, find the area of the "rectangle" as if there weren't different figure cut out of it:
(5+6+5)8
16(8)
128 yd²
Next, we are going to find the area of the four figures that are cut out from the rectangle. The circle at the bottom, the rectangle at the top, and the triangles on each side.
The first shape we can tackle will be the circle. The formula for finding the area of a circle is πr² or in this case 3.14r². The diameter of the circle is 6 yards, and half of the diameter is equal to the radius which gives us 3 yards as the length. Now simplify the expression:
3.14(3)²
3.14(9)
28.26 yd² is the area of the circle.
Next, we're going to find the area of the rectangle at the top. It's dimensions are 6 yards by 3 yards, which gives us an easy 18 yards² as the area (lxw).
Now we're going to solve for the area of the triangles. By the looks of the general dimensions of this shape, I am assuming these triangles are congruent to each other, which means we will only have to solve for its area once. To find the area of a triangle we have to use the expression: (lxw)/2. However, we don't know one of those dimensions. We know that the length is 8 yards as shown in the diagram, and by using the widths 2 yards and 5 yards, and their relation to the triangle, we can deduce the width is 3 yards. Now we have values necessary to simplify the expression:
(8x3)/2
24/2
12 yards² is the area of one triangle.
Because I stated previously that the triangles are congruent, they both have an area of 12 yards. Now we add the areas of each of the four figures, and subtract them from the area of our large rectangle:
128-(12+12+28.26+18)
128-70.26
57.74 yd² is the area of the shaded region
