Area of a Trapezoid - Examples, Exercises and Solutions

We use the formula (base+base) multiplied by the height and divided by 2.

Note that we are only provided with one base and it is not possible to determine the size of the other base.

Therefore, the area cannot be calculated.

Formula for the area of a trapezoid:

$\frac{(base+base)}{2}\times altura$

We substitute the data into the formula and solve:

$\frac{9+12}{2}\times5=\frac{21}{2}\times5=\frac{105}{2}=52.5$

We use the following formula to calculate the area of a trapezoid: (base+base) multiplied by the height divided by 2:

$\frac{(AB+DC)\times BE}{2}$

$\frac{(7+15)\times2}{2}=\frac{22\times2}{2}=\frac{44}{2}=22$

First, we need to remind ourselves of how to work out the area of a trapezoid:



Now let's substitute the given data into the formula:

(10+6)*5 =
2

Let's start with the upper part of the equation:

16*5 = 80

80/2 = 40

First, let's remind ourselves of the formula for the area of a trapezoid:

$A=\frac{\left(Base\text{ }+\text{ Base}\right)\text{ h}}{2}$

We substitute the given values into the formula:

(2.5+4)*6 =
6.5*6=
39/2 = 
19.5

We use the formula to calculate the area: (base+base) times the height divided by 2

$S=\frac{(AB+CD)\times h}{2}$

We input the data we are given:

$126=\frac{(AB+15)\times9}{2}$

We multiply the equation by 2:

$252=9AB+135$

$252-135=9AB$

$117=9AB$

We divide the two sections by 9

$13=AB$

We use the formula: (base + base) multiplied by height divided by 2:

$S=\frac{(AB+DC)\times h}{2}$

Keep in mind that AD is the height of a trapezoid:

We insert the existing data into the formula:

$S=\frac{(2+9)\times7}{2}$

$S=\frac{11\times7}{2}=\frac{77}{2}=38.5$

We use the formula to calculate the area: (base+base) times the height divided by 2

We replace the existing data:

$S=\frac{(AB+CD)\times h}{2}$

$30=\frac{(4+8)\times h}{2}$

We multiply the equation by 2:

$60=(4+8)h$

$60=12h$

We divide the two sections by 12:

$\frac{60}{12}=h$

$5=h$

The area of the trapezoid will be:

$S=\frac{(AB+DC)\times h}{2}$

We replace the known data in the formula:

$\frac{(5+7)}{2}\times\frac{8}{3}=$

$\frac{12\times8}{6}=$

$\frac{96}{6}=16$

Formula for the area of a trapezoid:

$\frac{(base+base)}{2}\times altura$

We substitute the data into the formula

$\frac{9+6}{2}\times h=30$

We solve:

$\frac{15}{2}\times h=30$

$7\frac{1}{2}\times h=30$

$h=\frac{30}{7\frac{1}{2}}$

$h=4$

The formula for the area of a trapezoid is:

$S=\frac{(AB+DC)\times h}{2}$

Since we are given AB and DC but not the height, we cannot calculate the area of the trapezoid.

We begin by inserting any given data into the formula to find the area of a trapezoid:

$S=\frac{(AB+CD)\times h}{2}$

We identify AD as the height of the trapezoid

$35=\frac{(6+8)\times AD}{2}$

$35=\frac{14}{2}AD$

$35=7AD$

We then divide the two sections by 7:

$5=AD$

Finally we calculate the perimeter by adding together all the sides as follows:

$5+6+8+5.5=11+8+5.5=19+5.5=24.5$

The area of the trapezoid will be equal to: $S=\frac{(AB+DC)}{2}\times h$

We insert the available data into the formula:

$1.375=\frac{AB+4}{2}\times0.5$

We then multiply by 2 in order to remove the fraction:

Lastly we again multiply by 2:

$5.5=AB+4$

$5.5-4=AB$

$1.5=AB$

The hexagon consists of two equal trapezoids, so we will strive to calculate the area of one of them and multiply it.

AFE is an isosceles triangle,

its height (FG) crosses the base exactly in the center, therefore:

$AG=GE$

$AG=\frac{1}{2}AE$

We replace and discover:

$AE=\frac{1}{2}\times12=6$

We replace the data in the formula for the area of a trapezoid:

$\frac{(base+base)}{2}\times altura$

$\frac{7+14}{2}\times6=\frac{21}{2}\times6=10.5\times6=63$

63 is the area of half of the hexagon, therefore:

$63\times2=126$

Since ABCD is a trapezoid, one can determine that:

$AD=BC=7$

Thus the formula to find the area will be

$$$S_{ABCD}=\frac{(AB+DC)\times h}{2}$

Since we are given the perimeter of the trapezoid, we can find$AB+DC$

$P_{ABCD}=7+AB+7+DC$

$34=14+AB+DC$

$34-14=AB+DC$

$20=AB+DC$

Now we will place the data we obtained into the formula in order to calculate the area of the trapezoid:

$S=\frac{20\times5}{2}=\frac{100}{2}=50$