The area of a trapezoid is equal to the average of the length of the two bases multiplied by the height.

The formula to find the area of a trapezoid is: $\displaystyle \left (\frac{base_{1} + base_{2}}{2}\right )* height$ 

In this problem, the lengths of the bases are $\displaystyle 10\: cm$ and $\displaystyle 20\: cm.$ Their average is $\displaystyle 15\: cm$. The height of the trapezoid is $\displaystyle 8\: cm.$

$\displaystyle 15\: cm\ast 8\: cm=120\: cm$

Remember: the answer to the problem should have units in cm² .

The area $\displaystyle A$ of a trapezoid is equal to the average of its two bases ($\displaystyle b_{1}$ and $\displaystyle b_{2}$) multiplied by its height $\displaystyle h$. Therefore:

$\displaystyle A=\frac{1}{2}(b_{1}+b_{2})h$

$\displaystyle A=\frac{1}{2}(4\:cm+8\:cm)5\:cm$

$\displaystyle A=\(6\:cm)5\:cm$

$\displaystyle A=30\:cm^{2}$

The area $\displaystyle A$ of a trapezoid is equal to the average of its two bases ($\displaystyle b_{1}$ and $\displaystyle b_{2}$) multiplied by its height $\displaystyle h$. Therefore:

$\displaystyle A=\frac{1}{2}(b_{1}+b_{2})h$

$\displaystyle A=\frac{1}{2}(10\:cm+12\:cm)8\:cm$

$\displaystyle A=\(11\:cm)8\:cm$

$\displaystyle A=88\:cm^{2}$

To find the area of a trapezoid, multiply one half (or 0.5, since we are working with decimals) by the sum of the lengths of its bases (the parallel sides) by its height (the perpendicular distance between the bases). This quantity is

$\displaystyle A = 0.5 \cdot (7.2 + 13.4) \cdot 10.6 =0.5 \cdot 20.6 \cdot 10.6 = 109.18\textrm{ m}^{2}$

The area of a trapezoid can be determined using the equation $\displaystyle A=\frac{1}{2}(b_1+b_2)h$.

$\displaystyle A=\frac{1}{2}(6+8)(4)$

$\displaystyle A=\frac{1}{2}(14)(4)$

$\displaystyle A=(7)(4)=28$

To find the area of a trapezoid, multiply the sum of the bases (the parallel sides) by the height (the perpendicular distance between the bases), and then divide by 2.

$\displaystyle A = \frac{1}{2} \cdot (7 + 15) \cdot 9 = \frac{1}{2} \cdot 22 \cdot 9 = 99 \textrm{ m}^2$

The length of a leg of $\displaystyle \Delta ECM$ is equal to the height of the orange region, which is a trapezoid. Call this length/height $\displaystyle h$.

Since the triangle is isosceles, then $\displaystyle CM = h$, and since $\displaystyle M$ is the midpoint of $\displaystyle \overline{CT}$, $\displaystyle MT = h$. Also, since opposite sides of a rectangle are congruent, 

$\displaystyle RE = CT = CM + MT = h + h = 2h$

Therefore, the orange region is a trapezoid with bases $\displaystyle h$ and $\displaystyle 2h$ and height $\displaystyle h$. Its area is 72, so we can set up and solve this equation using the area formula for a trapezoid:

 $\displaystyle \frac{1}{2} (B + b)h = 72$

$\displaystyle \frac{1}{2} (2h + h)h = 72$

$\displaystyle \frac{1}{2} (3h )h = 72$

$\displaystyle \frac{3}{2}h^{2} = 72$

$\displaystyle \frac{3}{2}h^{2} \cdot \frac{2}{3} = 72 \cdot \frac{2}{3}$

$\displaystyle h^{2}= 48$

$\displaystyle h = \sqrt {48}$

This is the length of one leg of the triangle.

Use the following formula, with $\displaystyle B = 36,b = 24,h=25$:

$\displaystyle A = \frac{1}{2} (B+b)h = \frac{1}{2} (36+24) \cdot 25 = 750$

Set  $\displaystyle B=200$, $\displaystyle b=100$, $\displaystyle h = 20$. 

The area of a trapezoid can be found using this formula:

$\displaystyle A = \frac{1}{2} (B+b)h = \frac{1}{2} (200+100) \cdot 20 = 3,000$

The area is 3,000 square inches.