Question

1. geometry write and solve an equation to find the value of x so that the figures have the same area. the area of a trapezoid is $\frac{1}{2}h(b_1 + b_2)$.

Explanation:

Step1: Calculate the area of the trapezoid

The formula for the area of a trapezoid is $A_{t}=\frac{1}{2}h(b_1 + b_2)$. Here, $h = 6$ in, $b_1=x$ in, $b_2 = 12$ in. So $A_{t}=\frac{1}{2}\times6\times(x + 12)=3(x + 12)=3x+36$.

Step2: Calculate the area of the rectangle

The formula for the area of a rectangle is $A_{r}=l\times w$. Here, $l = 12$ in, $w=x$ in. So $A_{r}=12x$.

Step3: Set the two - areas equal and solve for x

Since the areas are equal, we set $3x + 36=12x$. Subtract $3x$ from both sides: $36=12x-3x$. Simplify the right - hand side: $36 = 9x$. Divide both sides by 9: $x = 4$.

Answer:

$x = 4$