Trapeze - Examples, Exercises and Solutions

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

What is the perimeter of the trapezoid in the figure?

To find the perimeter we will add all the sides:

$4+5+9+6=9+9+6=18+6=24$

24

Look at the trapezoid in the diagram.

What is its perimeter?

To calculate the perimeter, we'll add up all the sides of the trapezoid:

7+10+7+12 =

36

And that's the solution!

36

$∢D=50°$

The isosceles trapezoid

What is $∢B$?

Let's recall that in an isosceles trapezoid, the sum of the two angles on each of the trapezoid's legs equals 180 degrees.

In other words:

$A+C=180$

$B+D=180$

Since angle D is known to us, we can calculate:

$180-50=B$

$130=B$

130°

Given: $∢C=2x$

$∢A=120°$

isosceles trapezoid.

Find x.

Given that the trapezoid is isosceles and the angles on both sides are equal, it can be argued that:

$∢C=∢D$

$∢A=∢B$

We know that the sum of the angles of a quadrilateral is 360 degrees.

Therefore we can create the formula:

$∢A+∢B+∢C+∢D=360$

We replace according to the existing data:

$120+120+2x+2x=360$

 $240+4x=360$

$4x=360-240$

$4x=120$

We divide the two sections by 4:

$\frac{4x}{4}=\frac{120}{4}$

$x=30$

30°

True OR False:

In all isosceles trapezoids the bases are equal.

True: in every isosceles trapezoid the base angles are equal to each other.

True

What is the area of the trapezoid in the figure?

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

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

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

$22$ cm².

The trapezoid ABCD is shown below. Given in cm:

Base AB = 6

Base DC = 10

Height (h) = 5

Calculate the area of the trapezoid.

Let's recall that the area of a trapezoid is:

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

40 cm²

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

$19\frac{1}{2}$

Look at the trapezoid in the figure.

The long base is 1.5 times longer than the short base.

Find the perimeter of the trapezoid.

First, we calculate the long base from the existing data:

Multiply the short base by 1.5:

$5\times1.5=7.5$

Now we will add up all the sides to find the perimeter:

$2+5+3+7.5=7+3+7.5=10+7.5=17.5$

17.5

The perimeter of the trapezoid in the diagram is 25 cm. Calculate the missing side.

We replace the data in the formula to find the perimeter:

$25=4+7+11+x$

$25=22+x$

$25-22=x$

$3=x$

$3$ cm

In an isosceles trapezoid ABCD

$∢B=3x$

$∢D=x$

Calculate the size of angle $∢B$.

To answer the question, we must know an important rule about isosceles trapezoids:

The sum of the angles that define each of the trapezoidal sides (not the bases) is equal to 180

Therefore:

∢B+∢D=180

3X+X=180

4X=180

X=45

It's important to remember that this is still not the solution, because we were asked for angle B,

Therefore:

3*45 = 135

And this is the solution!

135°

Do the diagonals of the trapezoid necessarily bisect each other?

The diagonals of an isosceles trapezoid are always equal to each other,

but they do not necessarily bisect each other.

(Reminder, "bisect" means that they meet exactly in the middle, meaning they are cut into two equal parts, two halves)

For example, the following trapezoid ABCD, which is isosceles, is drawn.

Using a computer program we calculate the center of the two diagonals,

And we see that the center points are not G, but the points E and F.

This means that the diagonals do not bisect.

No

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 insert the existing data into the formula:

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

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

$38.5$ cm².

The perimeter of the trapezoid equals 22 cm.

AB = 7 cm

AC = 3 cm

BD = 3 cm

What is the length of side CD?

Since we are given the perimeter of the trapezoid and not the length of CD, we can calculate:

$22=3+3+7+CD$

$22=CD+13$

$22-13=CD$

$9=CD$

9