Question

Ben says the area of the triangle equals the area of the trapezoid. If Ben's statement is true, what is the height, h, of the triangle? Explain. 10 m 10 m 4 m o is h 7 m and one triangle The area of the trapezoid is the sum of the area of one rectangle with area with area ; the sum of these areas is For the triangle, so h = (Type integer decimals

Answer 1

We start by calculating the area of the trapezoid.

This can be calculated as the sum of the area of the triangle and the rectangle.

The triangle has a base of 10-7=3 and a height of 4, and the rectangle has sides 4 and 7, so we can calculate the trapezoid area as:

$A_{}=A_t+A_r=\frac{3\cdot4}{2}+4\cdot7=6+28=34\operatorname{cm}^2$

The area of the trapezoid is 34 cm^2, as the area of the triangle is 6 cm^2 and the area of the rectangle is 28 cm^2.

Now, if the bigger triangle has also an area of 34 cm^2, we can write the area as:

$\begin{gathered} A=\frac{b\cdot h}{2}=\frac{10\cdot h}{2}=5h=34 \\ h=\frac{34}{5}=6.8\operatorname{cm} \end{gathered}$

To have the same area, the height of the triangle has to be h=6.8 cm.

Answer:

The area of the trapezoid is the sum of the area of one rectangle with area 28 cm^2 and one triangle with area 6 cm^2. The sum of this areas is 34 cm^2. For the triangle, area = 34 cm^2, so h=6.8 cm.