Question

If each unit is equivalent to 1 square inch, how many square inches of matting are used? A. 32 sq. Inches B. 36 square inches C. 40 square inches or D. 72 square inches

Answer 1

Answer:

B. 36 square inches

Step-by-step explanation:

we know that

The area of the mat is equal to the area of the rectangle containing a mat and a picture minus the area of the picture

The area of the picture is equal to the area of two trapezoids plus the area of the central rectangle

step 1

Find the area of the rectangle containing a mat and a picture

$A=(12)(6)=72\ in^2$

step 2

Find the area of the picture (two trapezoids plus the area of the central rectangle)

$A=\frac{1}{2}(4+2)(2)+\frac{1}{2}(4+2)(2)+(6)(4)$

$A=36\ in^2$

step 3

Subtract the areas

$72-36=36\ in^2$