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 $\displaystyle B = 36,b = 24,h=25$:

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

To solve, simply use the formula for the area of a trapezoid.

$\displaystyle b1=7, b2=9, h=2$

Thus,

$\displaystyle A=\frac{1}{2}(b1+b2)h=\frac{1}{2}(7+9)(2)=16$

The formula for area of a trapezoid is:

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

 where

$\displaystyle b_1=10, b_2=8, h=4$

therefore the area equation becomes,

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

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

$\displaystyle A = 36cm^{2}$

You recently bought a new bookshelf with a base in  the shape of an isosceles trapezoid. If the small base is 2 feet, the large base is 3 feet, and the depth is 8 inches, what is the area of the base of your new bookshelf?

To find the area of a trapezoid, we need to use the following formula:

$\displaystyle A_{trapezoid}=\frac{a+b}{2}*h$

Where a and b are the lengths of the bases, and h is the perpendicular distance from one base to another.

We are given a and b, and then h will be the same as our depth. The tricky part is realizing that our depth is in inches, while our base lengths are in feet. We need to convert 8 inches to feet:

$\displaystyle 8in*\frac{1ft}{12in}=\frac{8}{12}=\frac{2}{3}ft$

Next, plug it all into our equation up above.

$\displaystyle A_{trapezoid}=\frac{2+3}{2}*\frac{2}{3}=\frac{5}{2}*\frac{2}{3}$

$\displaystyle \frac{5}{2}*\frac{2}{3}=\frac{5}{3}ft^2$

So our answer is:

$\displaystyle \frac{5}{3}ft^2$

The easiest way to see this problem is to note that Quadrilateral $\displaystyle REMT$ has as its area that of Rectangle $\displaystyle RECT$ minus that of $\displaystyle \bigtriangleup ECM$.

The area of Rectangle $\displaystyle RECT$ is its length multiplied by its width:

$\displaystyle 2x \cdot \frac{1}{2} x = 2 \cdot \frac{1}{2} \cdot x \cdot x = x^{2}$

$\displaystyle M$ is the midpoint of $\displaystyle \overline{CT}$, so $\displaystyle \bigtriangleup ECM$ has as its base and height $\displaystyle \frac{1}{2} \cdot 2x =x$ and $\displaystyle \frac{1}{2} x$, respectively; 

its area is half their product, or 

$\displaystyle \frac{1}{2} \cdot x \cdot \frac{1}{2} x = \frac{1}{4} x^{2}$

The area of  Quadrilateral $\displaystyle REMT$ is 

$\displaystyle x^{2} - \frac{1}{4} x^{2} = \frac{3}{4} x^{2} = 1,200$, so

$\displaystyle \frac{3}{4} x^{2} \cdot \frac{4} {3} = 1,200\cdot \frac{4} {3}$

$\displaystyle x^{2} = 1,600$

$\displaystyle x =\sqrt{ 1,600} = 40$

The perimeter is equal to the sum of all of the sides.

$\displaystyle P=23\: cm$

$\displaystyle P=23\: cm=5+6+x+2x$

$\displaystyle 23=11+3x$

$\displaystyle 23-11=11+3x-11$

$\displaystyle 12=3x$

$\displaystyle \frac{12}{3}=\frac{3x}{3}$

$\displaystyle x=4$