Answer:
174 square yards
Step-by-step explanation:
You want the area of the given irregular figure.
Composition
The figure can be decomposed into several parts, and their areas added. In the process, we can make use of the relationship between the area of a triangle and the area of a rectangle.
Triangle
The area at the upper right of the figure can be considered as a triangle with base 8+7 = 15, and height 8. (All units are yards.) The area formula for a triangle is ...
A = 1/2(bh)
which tells you the area is equivalent to that of a rectangle with the same base and half the height. This area is shown by the dashed lines in the attachment. The triangle area is equivalent to a rectangle 15 wide and 4 high.
Rectangle
The area below the triangle is also 7+8 = 15 wide. The bounding rectangle is 9 high. This 15×9 rectangle has a 7×3 cutout at its lower left.
Total
So, the entire area can be considered as the sum of the areas of a rectangle 15 wide and 4 high, and a rectangle 15 wide and 9 high, less the area of the cutout, which is 7 wide and 3 high:
A = 15 × 4 +15 ×9 -7 ×3
= 15(4+9) -7(3)
= 195 -21 = 174 . . . . square yards
The area of the figure is 174 square yards.
