Examples with solutions for Area of a Triangle: Finding Area based off Perimeter and Vice Versa

Exercise #1

Calculate the area of the

triangle ABC given that its

perimeter equals 26.

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Video Solution

Step-by-Step Solution

Remember that the perimeter of a triangle is equal to the sum of all of the sides together,

We begin by finding side BC:

26=9+7+BC 26=9+7+BC

26=16+BC 26=16+BC

We then move the 16 to the left section and keep the corresponding sign:

2616=BC 26-16=BC

10=BC 10=BC

We use the formula to calculate the area of a triangle:

(the side * the height) /2

That is:

BC×AE2 \frac{BC\times AE}{2}

Lastly we insert the existing data:

10×62=602=30 \frac{10\times6}{2}=\frac{60}{2}=30

Answer

30

Exercise #2

The triangle ABC has a perimeter measuring 42 cm.

AD = 12

AC = 15

AB = 13

Calculate the area of the triangle.

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Video Solution

Step-by-Step Solution

Given that the perimeter of triangle ABC is 42.

We will use this data to find side CB:

13+15+CB=42 13+15+CB=42

CB+28=42 CB+28=42

CB=4228=14 CB=42-28=14

Now we can calculate the area of triangle ABC:

AD×BC2=12×142=1682=84 \frac{AD\times BC}{2}=\frac{12\times14}{2}=\frac{168}{2}=84

Answer

84 cm²

Exercise #3

Below is the right triangle ABD, which has a perimeter of 36 cm.

AB = 15

AC = 13

DC = 5

CB = 4

Work out the area of the triangle.

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Video Solution

Step-by-Step Solution

According to the data:

BD=4+5=9 BD=4+5=9

Now that we are given the perimeter of triangle ABD we can find the missing side AD:

AD+15+9=36 AD+15+9=36

AD+24=36 AD+24=36

AD=3624=12 AD=36-24=12

Thus we can calculate the area of triangle ABD:

AD×BD2=12×92=1082=54 \frac{AD\times BD}{2}=\frac{12\times9}{2}=\frac{108}{2}=54

Answer

54 cm²

Exercise #4

The perimeter of the triangle ABD shown below is 36 cm.

Given in cm:

AB = 15

AC = 13

DC = 5

CB = 4

Calculate the area of triangle ADC.

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Video Solution

Step-by-Step Solution

Using the given data of the triangle's perimeter we will first find the side AD by calculating the sum of all the sides of the triangle:

AD+9+15=36 AD+9+15=36

AD+24=36 AD+24=36

AD=3624=12 AD=36-24=12

Now that we know that AD is equal to 12, we are able to deduce that AD is also the height from BD since it forms a 90-degree angle.

If AD is the height from BD, it is also the height from DC.

Now we can calculate the area of the triangle ADC:

AD×DC2 \frac{AD\times DC}{2}

12×52=602=30 \frac{12\times5}{2}=\frac{60}{2}=30

Answer

30 cm²

Exercise #5

Calculate the area of the triangle ABC:

Given that: Perimeter=24

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Video Solution

Answer

22.5

Exercise #6

Calculate the area of the triangle ABC given that its perimeter is 18.

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Video Solution

Answer

27

Exercise #7

Calculate the area of the triangle ABC given that its perimeter is 14.

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Video Solution

Answer

12

Exercise #8

Calculate the area of the triangle ABC given that its perimeter is 15.

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Video Solution

Answer

12

Exercise #9

The perimeter of the triangle ABC equals 24.

What is its area?

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Video Solution

Answer

20

Exercise #10

Calculate the area of the triangle ABC given that its perimeter is 28.

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Video Solution

Answer

36

Exercise #11

The perimeter of triangle ABC is 23. Calculate its area.

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Video Solution

Answer

20

Exercise #12

Calculate the area of the triangle ABC:

Given that: Perimeter=12

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Video Solution

Answer

5

Exercise #13

The perimeter of triangle ABC is 23. Calculate its area.

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Video Solution

Answer

20

Exercise #14

Calculate the area of the triangle ABC given that its perimeter is 20.

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Video Solution

Answer

9

Exercise #15

The perimeter of triangle ABC is 26.

Calculate its area.

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Video Solution

Answer

30

Exercise #16

Given the triangle ADB right triangle.

The perimeter of the triangle is 30 cm

Given: AB=15 AC=13 DC=5 CB=4

Calculate the area of the triangle ABC

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Video Solution

Answer

24 cm²