Question

what is the area of this figure? write your answer using decimals, if necessary. square yards

Explanation:

Step1: Divide the figure into rectangles and a trapezoid

We can divide the given figure into two rectangles and a trapezoid.

Step2: Calculate the area of the first rectangle

The first rectangle has length \(l_1 = 5\) yd and width \(w_1=3\) yd. The area formula for a rectangle is \(A = l\times w\). So \(A_1=5\times3 = 15\) square - yards.

Step3: Calculate the area of the second rectangle

The second rectangle has length \(l_2=(2 + 3)=5\) yd and width \(w_2 = 2\) yd. So \(A_2=5\times2=10\) square - yards.

Step4: Calculate the area of the trapezoid

The trapezoid has bases \(b_1=(2 + 5)=7\) yd and \(b_2 = 7\) yd, and height \(h = 11\) yd. The area formula for a trapezoid is \(A=\frac{(b_1 + b_2)h}{2}\). So \(A_3=\frac{(7 + 7)\times11}{2}=\frac{14\times11}{2}=77\) square - yards.

Step5: Calculate the total area

The total area \(A = A_1+A_2+A_3\). Substitute the values: \(A=15 + 10+77=102\) square - yards.

Answer:

102