Question

The figure shows a kite inside a rectangle. Which expression represents the area of the shaded region?

Answer 1

Answer:

$4x^{2}\ units^{2}$

Step-by-step explanation:

we know that

The area of the shaded region is equal to the area of the rectangle minus the area of a kite

Step 1

Find the area of the rectangle

The area of the rectangle is equal to

$A=bh$

In this problem we have

$b=(3x+x)=4x\ units$

$h=(x+x)=2x\ units$

substitute

$A=(4x)(2x)=8x^{2}\ units^{2}$

Step 2

Find the area of a kite

The area of a kite is equal to

$A=\frac{1}{2}D1D2$

where D1 and D2 are the diagonals of a kite

In this problem we have

$D1=(3x+x)=4x\ units$

$D2=(x+x)=2x\ units$

substitute

$A=\frac{1}{2}(4x)(2x)=4x^{2}\ units^{2}$

Step 3

Find the area of the shaded region

$8x^{2}\ units^{2}-4x^{2}\ units^{2}=4x^{2}\ units^{2}$

Answer 2

1/2 of 4x+2x which is 4x