Area of a Triangle: Finding Area based off Perimeter and Vice Versa

Question 1

The triangle ABC has a perimeter measuring 42 cm.

AD = 12

AC = 15

AB = 13

Calculate the area of the triangle.

Question 2

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.

Question 3

Calculate the area of the

triangle ABC given that its

perimeter equals 26.

Question 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.

Question 5

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

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

Exercise #1

The triangle ABC has a perimeter measuring 42 cm.

AD = 12

AC = 15

AB = 13

Calculate the area of the triangle.

Video Solution

Step-by-Step Solution

Given that the perimeter of triangle ABC is 42.

We will use this data to find side CB:

$13+15+CB=42$

$CB+28=42$

$CB=42-28=14$

Now we can calculate the area of triangle ABC:

$\frac{AD\times BC}{2}=\frac{12\times14}{2}=\frac{168}{2}=84$

Answer

84 cm²

Exercise #2

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.

Video Solution

Step-by-Step Solution

According to the data:

$BD=4+5=9$

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

$AD+15+9=36$

$AD+24=36$

$AD=36-24=12$

Thus we can calculate the area of triangle ABD:

$\frac{AD\times BD}{2}=\frac{12\times9}{2}=\frac{108}{2}=54$

Answer

54 cm²

Exercise #3

Calculate the area of the

triangle ABC given that its

perimeter equals 26.

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:

$26=9+7+BC$

$26=16+BC$

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

$26-16=BC$

$10=BC$

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

(the side * the height) /2

That is:

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

Lastly we insert the existing data:

$\frac{10\times6}{2}=\frac{60}{2}=30$

Answer

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.

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:

$AD+9+15=36$

$AD+24=36$

$AD=36-24=12$

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:

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

$\frac{12\times5}{2}=\frac{60}{2}=30$

Answer

30 cm²

Exercise #5

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

Video Solution

Answer

Question 1

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

Question 2

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

Question 3

The perimeter of the triangle ABC equals 24.

What is its area?

Question 4

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

Question 5

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

Exercise #6

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

Video Solution

Answer

Exercise #7

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

Video Solution

Answer

Exercise #8

The perimeter of the triangle ABC equals 24.

What is its area?

Video Solution

Answer

Exercise #9

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

Video Solution

Answer

Exercise #10

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

Video Solution

Answer

Question 1

Calculate the area of the triangle ABC:

Given that: Perimeter=12

Question 2

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

Question 3

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

Question 4

The perimeter of triangle ABC is 26.

Calculate its area.

Question 5

Calculate the area of the triangle ABC:

Given that: Perimeter=24

Exercise #11

Calculate the area of the triangle ABC:

Given that: Perimeter=12

Video Solution

Answer

Exercise #12

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

Video Solution

Answer

Exercise #13

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

Video Solution

Answer

Exercise #14

The perimeter of triangle ABC is 26.

Calculate its area.

Video Solution

Answer

Exercise #15

Calculate the area of the triangle ABC:

Given that: Perimeter=24

Video Solution

Answer

22.5

Question 1

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

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

Video Solution

Answer

24 cm²