Question

Find the area of the shaded region in square units. Show your reasoning.

Answer 1

40 square units

Explanation:

First of all, lets say that square has side
`l`, so, the area unit is
`l^2`

the diagonal's square is
`l√(2)`

CALCULATION OF TRIANGLES'S AREA (there are 4 triangles)

`A_(triangles)=4*base*heigh*0.5=2*(l√(2) )(2l√(2) )=8l^2`

CALCULATION OF MAIN SQUARE AREA

`A_(square)=side*side=(4√(2) l)(4√(2) l)=32l^2`

TOTAL AREA

`A_(total)=A_(triangles)+A_(square)=8l^2+32l^2=40l^2`