Area - Examples, Exercises and Solutions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?

Remember that the formula for the area of a rectangle is width times height

We are given that the width of the rectangle is 6

and that the length of the rectangle is 4

 Therefore we calculate:

6*4=24

24 cm²

Calculate the area of the following triangle:

The formula for calculating the area of a triangle is:

(the side * the height from the side down to the base) /2

That is:

$\frac{BC\times AE}{2}$

We insert the existing data as shown below:

$\frac{4\times5}{2}=\frac{20}{2}=10$

10

Given the rhombus in the drawing:

What is the area?

Let's remember that there are two ways to calculate the area of a rhombus:

The first is the side times the height of the side.

The second is diagonal times diagonal divided by 2.

Since we are given both diagonals, we calculate it the second way:

$\frac{7\times4}{2}=\frac{28}{2}=14$

14

Given the following rectangle:

Find the area of the rectangle.

Let's calculate the area of the rectangle by multiplying the length by the width:

$2\times5=10$

10

Look at the rectangle ABCD below.

Side AB is 4.5 cm long and side BC is 2 cm long.

What is the area of the rectangle?

We begin by multiplying side AB by side BC

We then substitute the given data and we obtain the following:

$4.5\times2=9$

Hence the area of rectangle ABCD equals 9

9 cm²

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 width of a rectangle is equal to 15 cm and its length is 3 cm.

Calculate the area of the rectangle.

To calculate the area of the rectangle, we multiply the length by the width:

$15\times3=45$

45

What is the area of the given triangle?

This question is a bit confusing. We need start by identifying which parts of the data are relevant to us.

Remember the formula for the area of a triangle:

The height is a straight line that comes out of an angle and forms a right angle with the opposite side.

In the drawing we have a height of 6.

It goes down to the opposite side whose length is 5.

And therefore, these are the data points that we will use.

We replace in the formula:

$\frac{6\times5}{2}=\frac{30}{2}=15$

15

Calculate the area of the triangle ABC using the data in the figure.

First, let's remember the formula for the area of a triangle:

(the side * the height that descends to the side) /2

In the question, we have three pieces of data, but one of them is redundant!

We only have one height, the line that forms a 90-degree angle - AD,

The side to which the height descends is CB,

Therefore, we can use them in our calculation:

$\frac{CB\times AD}{2}$

$\frac{8\times9}{2}=\frac{72}{2}=36$

36 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

$19\frac{1}{2}$

ABCD is a rectangle.

Given in cm:

AB = 7

BC = 5

Calculate the area of the rectangle.

Let's calculate the area of the rectangle by multiplying the length by the width:

$AB\times BC=7\times5=35$

35

Calculate the area of the following triangle:

The formula for the area of a triangle is

$A = \frac{h\cdot base}{2}$

Let's insert the available data into the formula:

(7*6)/2 =

42/2 =

21

21

Look at rectangle ABCD below.

Side AB is 10 cm long and side BC is 2.5 cm long.

What is the area of the rectangle?

Let's multiply side AB by side BC

We'll substitute the known data and get:

$10\times2.5=25$

The area of rectangle ABCD equals 25

25 cm²

Shown below is the deltoid ABCD.

The diagonal AC is 8 cm long.

The area of the deltoid is 32 cm².

Calculate the diagonal DB.

First, we recall the formula for the area of a kite: multiply the lengths of the diagonals by each other and divide the product by 2.

We substitute the known data into the formula:

 $\frac{8\cdot DB}{2}=32$

We reduce the 8 and the 2:

$4DB=32$

Divide by 4

$DB=8$

8 cm

Look at the rectangle ABCD below.

Given in cm:

AB = 10

BC = 5

Calculate the area of the rectangle.

Let's calculate the area of the rectangle by multiplying the length by the width:

$AB\times BC=10\times5=50$

50