what is the area of this figure?\nif necessary, round your answer to the nearest hundredth.\nsquare yards

Explanation:

Step1: Calculate the area of the first rectangle

The first rectangle has length (9) yd and width (2) yd. The area of a rectangle is (A = l\times w), so (A_1=9\times2 = 18) square yards.

Step2: Calculate the area of the second rectangle

The second rectangle has length (7) yd and width (7) yd. Using the formula (A = l\times w), (A_2 = 7\times7=49) square yards.

Step3: Calculate the area of the third rectangle

The third rectangle has length (9 - 2=7) yd and width (4) yd. Using the formula (A = l\times w), (A_3=7\times4 = 28) square yards.

Step4: Calculate the area of the semicircle

The diameter of the semicircle is (9 - 2=7) yd, so the radius (r=\frac{7}{2}=3.5) yd. The area of a full - circle is (A=\pi r^{2}), and the area of a semicircle is (A_{semicircle}=\frac{1}{2}\pi r^{2}). Substituting (r = 3.5) yd, (A_{semicircle}=\frac{1}{2}\times\pi\times(3.5)^{2}=\frac{1}{2}\times\pi\times12.25\approx19.24) square yards.

Step5: Sum up the areas

(A=A_1 + A_2+A_3+A_{semicircle}) (A=18 + 49+28+19.24) (A=114.24) square yards.

Answer:

(114.24)