Question

finding the area of composite figures. which expression can be used to find the area of the composite figure? 4x, 2x + 2x^2, x^2 + 2x, 3x^2

Explanation:

Step1: Divide the composite figure

The figure can be divided into a rectangle and two congruent right - triangles.

Step2: Calculate the area of the rectangle

The base of the rectangle is $2x$ and the height is $x$, so the area of the rectangle $A_{r}=2x\times x = 2x^{2}$.

Step3: Calculate the area of one right - triangle

The base and height of each right - triangle are $x$. The area of a right - triangle is $A_{t}=\frac{1}{2}\times x\times x=\frac{1}{2}x^{2}$. The combined area of two right - triangles is $2\times\frac{1}{2}x^{2}=x^{2}$.

Step4: Calculate the area of the composite figure

The area of the composite figure $A = A_{r}+A_{t}=2x^{2}+x^{2}=3x^{2}$.

Answer:

$3x^{2}$