Question

what is the area of this figure?

Explanation:

Step1: Divide the figure into rectangles and a triangle

We can divide the figure into two rectangles and a right - triangle.

Step2: Calculate the area of the first rectangle

The first rectangle has length $l_1=(6 + 3)=9$ inches and width $w_1 = 5$ inches. The area formula for a rectangle is $A = l\times w$. So, $A_1=9\times5 = 45$ square inches.

Step3: Calculate the area of the second rectangle

The second rectangle has length $l_2=2$ inches and width $w_2 = 6$ inches. Using the rectangle area formula, $A_2=2\times6=12$ square inches.

Step4: Calculate the area of the triangle

The base of the triangle $b = 7$ inches and the height $h=(5 + 11-6)=10$ inches. The area formula for a triangle is $A=\frac{1}{2}bh$. So, $A_3=\frac{1}{2}\times7\times10 = 35$ square inches.

Step5: Calculate the total area of the figure

The total area $A = A_1+A_2+A_3$. So, $A=45 + 12+35=92$ square inches.

Answer:

92 square inches