Area - Examples, Exercises and Solutions

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

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

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.

Calculate the area of the triangle below, if possible.

The formula to calculate the area of a triangle is:

(side * height corresponding to the side) / 2

Note that in the triangle provided to us, we have the length of the side but not the height.

That is, we do not have enough data to perform the calculation.

Cannot be calculated

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

Given the following rectangle:

Find the area of the rectangle.

We will use the formula to calculate the area of a rectangle: length times width

$9\times6=54$

54

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:

$4\times8=32$

32

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:

$11\times7=77$

77

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

Look at the circle in the figure:

The radius is equal to 7.

What is the area of the circle?

Remember that the formula for the area of a circle is

πR²

We replace the data we know:

π7²

π49

49π

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

Look at the square below:

What is the area of the square?

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=9^2=81$

$81$

Given the square:

What is the area of the square?

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=7^2=49$

$49$

Look at the square below:

What is the area of the square?

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the diagram provides us with one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=3^2=9$

$9$

Look at the square below:

What is the area of the square?

The area of the square is equal to the side of the square raised to the second power.

That is:

$A=L^2$

Since the drawing gives us one side of the square, and in a square all sides are equal, we will solve the area of the square as follows:

$A=10^2=100$

$100$