Question

Please help! Which expression can be used to find the area of the composite figure?

A. 4x

B. 2x+2x^2

C. x^2+2x

D. 3x^2

The answer is 3x^2

Answer 1

The Correct Answer is 3x2

Answer 2

The correct option is D.

Explanation:

The given figure contains two congruent triangle and one rectangle. The length of the rectangle is 2x and width of the rectangle is x. The height and base of the triangle is same, i.e. x.

The area of rectangle is

`A_1=l* w`

`A_1=2x* x=2x^2`

The area of triangle is

`A_2=(1)/(2)* base* height`

`A_2=(1)/(2)* x* x=(x^2)/(2)`

The area of given figure is

Total Area = Area of rectangle + 2(Area of a triangle)

`Area=2x^2+2((x^2)/(2))`

`Area=2x^2+x^2=3x^2`

The area of given figure is
`3x^2`, therefore the correct option is D.