Examples with solutions for Area of a Triangle: Applying the formula

Exercise #1

What is the area of the given triangle?

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Video Solution

Step-by-Step Solution

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:

A1- How to find the area of a triangleThe 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:

6×52=302=15 \frac{6\times5}{2}=\frac{30}{2}=15

Answer

15

Exercise #2

What is the area of the triangle in the drawing?

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Video Solution

Step-by-Step Solution

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

5×72=352=17.5 \frac{5\times7}{2}=\frac{35}{2}=17.5

Answer

17.5

Exercise #3

The triangle ABC is given below.
AC = 10 cm

AD = 3 cm

BC = 11.6 cm
What is the area of the triangle?

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Video Solution

Step-by-Step Solution

The triangle we are looking at is the large triangle - ABC

The triangle is formed by three sides AB, BC, and CA.

Now let's remember what we need for the calculation of a triangular area:

(side x the height that descends from the side)/2

Therefore, the first thing we must find is a suitable height and side.

We are given the side AC, but there is no descending height, so it is not useful to us.

The side AB is not given,

And so we are left with the side BC, which is given.

From the side BC descends the height AD (the two form a 90-degree angle).

It can be argued that BC is also a height, but if we delve deeper it seems that CD can be a height in the triangle ADC,

and BD is a height in the triangle ADB (both are the sides of a right triangle, therefore they are the height and the side).

As we do not know if the triangle is isosceles or not, it is also not possible to know if CD=DB, or what their ratio is, and this theory fails.

Let's remember again the formula for triangular area and replace the data we have in the formula:

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

Now we replace the existing data in this formula:

CB×AD2 \frac{CB\times AD}{2}

11.6×32 \frac{11.6\times3}{2}

34.82=17.4 \frac{34.8}{2}=17.4

Answer

17.4

Exercise #4

Calculate the area of the following triangle:

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Video Solution

Step-by-Step Solution

The formula for the area of a triangle is

A=hbase2 A = \frac{h\cdot base}{2}

Let's insert the available data into the formula:

(7*6)/2 =

42/2 =

21

Answer

21

Exercise #5

Calculate the area of the following triangle:

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Video Solution

Step-by-Step Solution

The formula for calculating the area of a triangle is:

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

That is:

BC×AE2 \frac{BC\times AE}{2}

We insert the existing data as shown below:

4×52=202=10 \frac{4\times5}{2}=\frac{20}{2}=10

Answer

10

Exercise #6

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

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Video Solution

Step-by-Step Solution

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:

CB×AD2 \frac{CB\times AD}{2}

8×92=722=36 \frac{8\times9}{2}=\frac{72}{2}=36

Answer

36 cm²

Exercise #7

Calculate the area of the right triangle below:

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Video Solution

Step-by-Step Solution

Due to the fact that AB is perpendicular to BC and forms a 90-degree angle,

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

Hence we can calculate the area as follows:

AB×BC2=8×62=482=24 \frac{AB\times BC}{2}=\frac{8\times6}{2}=\frac{48}{2}=24

Answer

24 cm²

Exercise #8

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

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Video Solution

Answer

14

Exercise #9

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

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Video Solution

Answer

24

Exercise #10

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

101010999AAABBBCCC

Video Solution

Answer

45

Exercise #11

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

101010222AAABBBCCC

Video Solution

Answer

10

Exercise #12

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

666888AAABBBCCC

Video Solution

Answer

24

Exercise #13

Calculate the area of the triangle, if possible.

777444

Video Solution

Answer

14

Exercise #14

Calculate the area of the triangle below, if possible.

3.53.53.5666

Video Solution

Answer

10.5

Exercise #15

Calculate the area of the triangle below, if possible.

8.68.68.6777555

Video Solution

Answer

17.5

Exercise #16

Calculate the area of the triangle below, if possible.

666777444

Video Solution

Answer

14

Exercise #17

Calculate the area of the triangle below, if possible.

555999666

Video Solution

Answer

15

Exercise #18

Calculate the area of the following triangle:

444444AAABBBCCCEEE

Video Solution

Answer

8

Exercise #19

Calculate the area of the following triangle:

888101010AAABBBCCCEEE

Video Solution

Answer

40

Exercise #20

Calculate the area of the following triangle:

4.54.54.5777AAABBBCCCEEE

Video Solution

Answer

15.75