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

Answer

Explanation:

Step1: Divide the figure into shapes

Divide the figure into a rectangle, a square and a triangle.

Step2: Calculate the area of the rectangle

The rectangle on the right - hand side has length (l = 8) yd and width (w=4) yd. The area of a rectangle (A_{1}=l\times w), so (A_{1}=8\times4 = 32) square yards.

Step3: Calculate the area of the square

The square in the middle has side - length (s = 2) yd. The area of a square (A_{2}=s^{2}), so (A_{2}=2\times2=4) square yards.

Step4: Calculate the area of the rectangle on the left

The rectangle on the left has length (l = 8) yd and width (w = 2) yd. The area of a rectangle (A_{3}=l\times w), so (A_{3}=8\times2 = 16) square yards.

Step5: Calculate the area of the triangle

The base of the triangle (b=8) yd and the height (h = 8) yd. The area of a triangle (A_{4}=\frac{1}{2}\times b\times h), so (A_{4}=\frac{1}{2}\times8\times8=32) square yards.

Step6: Calculate the total area

The total area (A = A_{1}+A_{2}+A_{3}+A_{4}). Substitute the values: (A=32 + 4+16+32). [A=(32+4)+16 + 32=36+16+32=84] square yards.