Question

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

Explanation:

Step1: Divide the figure into known - shapes

The figure can be divided into a rectangle, a square, and a triangle.

Step2: Calculate the area of the rectangle

The rectangle has length \(l = 8\) in and width \(w=7\) in. The area of a rectangle \(A_{1}=l\times w\), so \(A_{1}=8\times7 = 56\) square - inches.

Step3: Calculate the area of the square

The square has side - length \(s = 5\) in. The area of a square \(A_{2}=s^{2}\), so \(A_{2}=5\times5=25\) square - inches.

Step4: Calculate the area of the triangle

The triangle has base \(b = 4\) in and height \(h = 2 + 5=7\) in. The area of a triangle \(A_{3}=\frac{1}{2}\times b\times h\), so \(A_{3}=\frac{1}{2}\times4\times7 = 14\) square - inches.

Step5: Calculate the total area of the figure

The total area \(A = A_{1}+A_{2}+A_{3}\). Substitute the values: \(A=56 + 25+14=95\) square - inches.

Answer:

95