Question

Calculate the missing area

Answer 1

The missing area is 28 square inches

Explanation:

see the attached figure with letters to better understand the problem

we know that

The area of triangle is given by the formula

`A=(1)/(2)(b)(h)`

In this problem

In each side of the square there are two triangles with the same area, because they have the same base and the same height

so

`16+20+32=C+2D+2A+B`

`68=C+2D+2A+B`

Group terms

`(B+C)=68-2D-2A`

`(B+C)=68-2(D+A)` ----> equation A

we have that

`A+D=20\ cm^2` ----> equation B see the picture

substitute equation B in equation A

`(B+C)=68-2(20)=28\ cm^2`

therefore

The missing area is 28 square inches