Area of a Trapezoid - Examples, Exercises and Solutions

Calculate the area of the trapezoid.

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.

Cannot be calculated.

Given the trapezoid:

What is the area?

Formula for the area of a trapezoid:

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

We substitute the data into the formula and solve:

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

52.5

The trapezoid ABCD is shown below.

AB = 2.5 cm

DC = 4 cm

Height (h) = 6 cm

Calculate the area of the trapezoid.

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

$19\frac{1}{2}$

What is the area of the trapezoid in the figure?

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

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

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

$22$ cm².

Given the trapezoid in front of you:

Given h=9, DC=15.

Since the area of the trapezoid ABCD is equal to 126.

Find the length of the side AB.

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

$13=AB$

13

The trapezoid ABCD is shown below.

AB = 4 cm

DC = 8 cm

Area of the trapezoid (S) = 30 cm²

Calculate the height of the trapezoid.

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:

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

$5=h$

5

What is the area of the trapezoid in the figure?

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 replace the existing data in the formula:

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

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

$38.5$ cm².

ABCD is a trapezoid.

AB = 4 cm

DC = 7 cm

BK = 6 cm

Can the trapezoidal area formula be applied? If so, apply it and calculate.

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.

It cannot be applied.

Given the following trapezoid:

Find the area of the trapezoid ABCD.

The area of the trapezoid will be:

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

We replace the known data in the formula:

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

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

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

16

Given the trapezoid:

What is the height?

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:

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

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

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

$h=4$

4

Look at the trapezoid in the figure.

Its area is equal to 35 cm².

Calculate its perimeter.

We use the formula to find the area of a trapezoid and replace the existing data in it:

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

We recognize that AD is the height of the trapezoid

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

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

$35=7AD$

We divide the two sections by 7:

$5=AD$

Now we calculate the perimeter by adding all the sides:

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

$24.5$ cm

The area of the trapezoid in the diagram is 1.375 cm².

Work out the length of the side marked in red.

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

We replace the data we have in the formula:

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

We multiply by 2 to get rid of the fraction:

$2.75=(AB+4)\times\frac{1}{2}$

We multiply by 2:

$5.5=AB+4$

$5.5-4=AB$

$1.5=AB$

$1.5$ cm

Below is an equilateral hexagon.

AB = 7
FC = 14
AE = 12.124

What is the area of the hexagon?

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:

$63\times2=126$

127.3

Shown below is the isosceles trapezoid ABCD.

Given in cm:
BC = 7  

Height of the trapezoid (h) = 5

Perimeter of the trapezoid (P) = 34

Calculate the area of the trapezoid.

Since ABCD is a trapezoid, it can be argued that:

$AD=BC=7$

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 received in the formula to calculate the area of the trapezoid:

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

50

The trapezoid DECB forms part of triangle ABC.

AB = 6 cm
AC = 10 cm

Calculate the area of the trapezoid DECB, given that DE divides both AB and AC in half.

DE crosses AB and AC, that is to say:

$AD=DB=\frac{1}{2}AB=\frac{1}{2}\times6=3$

$AE=EC=\frac{1}{2}AC=\frac{1}{2}\times10=5$

Now let's look at triangle ADE, two sides of which we have already calculated.

Now we can find the third side DE using the Pythagorean theorem:

$AD^2+DE^2=AE^2$

We substitute our values into the formula:

$3^2+DE^2=5^2$

$9+DE^2=25$

$DE^2=25-9$

$DE^2=16$

We extract the root:

$DE=\sqrt{16}=4$

Now let's look at triangle ABC, two sides of which we have already calculated.

Now we can find the third side (BC) using the Pythagorean theorem:

$AB^2+BC^2=AC^2$

We substitute our values into the formula:

$6^2+BC^2=10^2$

$36+BC^2=100$

$BC^2=100-36$

$BC^2=64$

We extract the root:

$BC=\sqrt{64}=8$

Now we have all the data needed to calculate the area of the trapezoid DECB using the formula:

(base + base) multiplied by the height divided by 2:

Keep in mind that the height in the trapezoid is DB.

$S=\frac{(4+8)}{2}\times3$

$S=\frac{12\times3}{2}=\frac{36}{2}=18$

18