Question

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

Answer 1

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

Answer 2

`4x^(2)\ units^(2)`

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=(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=(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)`