Question

place the orange triangle (square symbols) directly next to the green triangle so that the two triangles together make a rectangle. the total area of this rectangle is , which is the area of the green triangle.

Explanation:

Step1: Recall area relationship

A rectangle can be formed by two congruent right - angled triangles. If we assume the base of the green triangle is $b$ and height is $h$, the area of a triangle is $A_{triangle}=\frac{1}{2}bh$.

Step2: Calculate rectangle area

The area of the rectangle formed by the two congruent triangles (orange and green) with base $b$ and height $h$ is $A_{rectangle}=bh$.

Step3: Find the ratio

We divide the area of the rectangle by the area of the green triangle. $\frac{A_{rectangle}}{A_{triangle}}=\frac{bh}{\frac{1}{2}bh} = 2$.

Answer:

The total area of this rectangle is $bh$, which is $2$ times the area of the green triangle.