Question

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

Answer 1

Answer:

40 square units

Step-by-step explanation:

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

the diagonal's square is $l\sqrt{2}$

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

$A_{triangles}=4*base*heigh*0.5=2*(l\sqrt{2} )(2l\sqrt{2} )=8l^2$

CALCULATION OF MAIN SQUARE AREA

$A_{square}=side*side=(4\sqrt{2} l)(4\sqrt{2} l)=32l^2$

TOTAL AREA

$A_{total}=A_{triangles}+A_{square}=8l^2+32l^2=40l^2$