In this article, we will briefly learn everything necessary about triangles and also practice with some exercises!

Let's get started!

In this article, we will briefly learn everything necessary about triangles and also practice with some exercises!

Let's get started!

Question 1

Calculate the area of the right triangle below:

Question 2

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

Question 3

Calculate the area of the following triangle:

Question 4

Calculate the area of the triangle below, if possible.

Question 5

Given the triangle:

What is its perimeter?

Calculate the area of the right triangle below:

As we see that AB is perpendicular to BC and forms a 90-degree angle

It can be argued that AB is the height of the triangle.

Then we can calculate the area as follows:

$\frac{AB\times BC}{2}=\frac{8\times6}{2}=\frac{48}{2}=24$

24 cm²

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

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:

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

Now we replace the existing data:

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

10

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

Given the triangle:

What is its perimeter?

The perimeter of a triangle is equal to the sum of all its sides together:

$11+7+13=11+20=31$

31

Question 1

Look at the triangle below:

What is the perimeter of the triangle?

Question 2

What is the area of the given triangle?

Question 3

Angle A equals 56°.

Angle B equals 89°.

Angle C equals 17°.

Can these angles make a triangle?

Question 4

Angle A equals 90°.

Angle B equals 115°.

Angle C equals 35°.

Can these angles form a triangle?

Question 5

Angle A is equal to 30°.

Angle B is equal to 60°.

Angle C is equal to 90°.

Can these angles form a triangle?

Look at the triangle below:

What is the perimeter of the triangle?

The perimeter of the triangle is equal to the sum of all sides together, therefore:

$6+8+10=14+10=24$

24

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

Angle A equals 56°.

Angle B equals 89°.

Angle C equals 17°.

Can these angles make a triangle?

We add the three angles to see if they are equal to 180 degrees:

$56+89+17=162$

The sum of the given angles is not equal to 180, so they cannot form a triangle.

No.

Angle A equals 90°.

Angle B equals 115°.

Angle C equals 35°.

Can these angles form a triangle?

We add the three angles to see if they are equal to 180 degrees:

$90+115+35=240$

The sum of the given angles is not equal to 180, so they cannot form a triangle.

No.

Angle A is equal to 30°.

Angle B is equal to 60°.

Angle C is equal to 90°.

Can these angles form a triangle?

We add the three angles to see if they equal 180 degrees:

$30+60+90=180$

The sum of the angles equals 180, so they can form a triangle.

Yes

Question 1

What is the area of the triangle in the drawing?

Question 2

What kind of triangle is the following

Question 3

Given an equilateral triangle:

What is its perimeter?

Question 4

Given the isosceles triangle,

What is its perimeter?

Question 5

Look at the isosceles triangle below:

What is its perimeter?

What is the area of the triangle in the drawing?

First, we will identify the data points we need to be able to find the area of the triangle.

the formula for the area of the triangle: height*opposite side / 2

Since it is a right triangle, we know that the straight sides are actually also the heights between each other, that is, the side that measures 5 and the side that measures 7.

We multiply the legs and divide by 2

$\frac{5\times7}{2}=\frac{35}{2}=17.5$

17.5

What kind of triangle is the following

Since in the given triangle all angles are equal, all sides are also equal.

It is known that in an equilateral triangle the measure of the angles will always be equal to 60° since the sum of the angles in a triangle is 180 degrees:

$60+60+60=180$

Therefore, it is an equilateral triangle.

Equilateral triangle

Given an equilateral triangle:

What is its perimeter?

Since the triangle is equilateral, that is, all sides are equal to each other.

The perimeter of the triangle is equal to the sum of all sides together, the perimeter of the triangle in the drawing is equal to:

$5+5+5=15$

15

Given the isosceles triangle,

What is its perimeter?

Since the triangle is isosceles, that means its two legs are equal to each other.

Therefore, the base is 7 and the other two sides are 12.

The perimeter of a triangle is equal to the sum of all sides together:

$12+12+7=24+7=31$

31

Look at the isosceles triangle below:

What is its perimeter?

Since we are referring to an isosceles triangle, the two legs are equal to each other.

In the drawing, they give us the base which is equal to 4 and one side is equal to 6, therefore the other side is also equal to 6.

The perimeter of the triangle is equal to the sum of the sides and therefore:

$6+6+4=12+4=16$

16