A trapezoid is a four-sided shape with straight sides that has a pair of opposite parallel sides. The other sides may or may not be parallel. A square and a rectangle are both considered trapezoids.

The formula for the area of a trapezoid is:

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

where $\displaystyle b_{1}$ is the value of the top base, $\displaystyle b_{2}$ is value of the bottom base, and $\displaystyle h$ is the value of the height.

Plugging in our values, we get:

$\displaystyle A = \frac{1}{2} (8\: m + 10\: m)(4\: m)$

$\displaystyle A = \frac{1}{2} (18\: m)(4\: m)$

$\displaystyle A = (9\: m)(4\: m) = 36\: m^2$

The formula for the area of a trapezoid is the average of the bases times the height,

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

Looking at this problem and when the appropriate values are plugged in, the formula yields:

 $\displaystyle A=(\frac{10+24}{2})7$

$\displaystyle A=\frac{34}{2}\cdot 7$

$\displaystyle A=\frac{238}{2}=119$

To find the height, we must introduce two variables, $\displaystyle b_{1}, b_{2}$, each representing the bases of the triangles on the outside, so that $\displaystyle b_{1}+b_{2}+11=25, b_{1}+b_{2}=14$. (Equation 1)

The next step is to set up two Pythagorean Theorems, 

$\displaystyle 13^2=b_{1}^2+h^2, 15^2=b_{2}^2+h^2$ (Equation 2, 3)

The next step is a substitution from the first equation, 

$\displaystyle b_{1}=14-b_{2}, b_{1}^2=196-28b_{2}+b_{2}^2$ (Equation 4)

and plugging it in to the second equation, yielding 

$\displaystyle 13^2=196-28b_{2}+b_{2}^2+h^2$ (Equation 5)

The next step is to substitute from Equation 3 into equation 5, 

$\displaystyle h^2=15^2-b_{2}^2$, $\displaystyle 169=196-28b_{2}+b_{2}^2+225-b_{2}^2$ which simplifies to

$\displaystyle -252=-28b_{2}, b_{2}=9$

Once we have one of the bases, just plug into the Pythagorean Theorem, $\displaystyle 225=81+h^2, 144=h^2, h=12$

An isosceles trapezoid has two sides that are the same length and those are not the bases, so the bases are 10 and 20.

The area of the trapezoid then is:

$\displaystyle A=\frac{b_{1}+b_{2}}{2}h=\frac{10+20}{2}12=15 \cdot 12=180$

The formula for finding the area of a trapezoid is:

$\displaystyle A=\frac{1}{2}(b1+b2)h$

Substitute the given values to find the area.

$\displaystyle A=\frac{1}{2}(20+10)(10)$

$\displaystyle A= \frac{1}{2}(30)(10)$

$\displaystyle A=\frac{1}{2}(300)$

$\displaystyle A=150$

The formula for the area of a trapezoid is:

$\displaystyle A = \frac{a + b}{2}h$

Where $\displaystyle a$ and $\displaystyle b$ are the bases and $\displaystyle h$ is the height. Using this formula and the given values, we get:

$\displaystyle A = \frac{12\:cm + 15\:cm}{2}\left ( 7\:cm) = 94.5\:cm^2$

The formula for the area of a trapezoid is:

$\displaystyle A = \frac{a + b}{2}h$

Where $\displaystyle a$ and $\displaystyle b$ are the bases and $\displaystyle h$ is the height. Using this formula and the given values, we get:

The formula for the area of a trapezoid is:

$\displaystyle A = \frac{a + b}{2}h$

Where $\displaystyle a$ and $\displaystyle b$ are the bases and $\displaystyle h$ is the height. Using this formula and the given values, we get:

$\displaystyle A = \frac{13\:units + 29\:units}{2}\left ( 15\:units ) = 315\:units^2$

The formula for the area of a trapezoid is:

$\displaystyle A = \frac{a + b}{2}h$

Where $\displaystyle a$ and $\displaystyle b$ are the bases and $\displaystyle h$ is the height. Using this formula and the given values, we get:

$\displaystyle A = \frac{4\:units + 10\:units}{2}\left ( 4\:units\right ) = 28\:units^2$