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

The triangle ABC has a perimeter measuring 42 cm.

AD = 12

AC = 15

AB = 13

Calculate the area of the triangle.

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:

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

84 cm²

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.

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:

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

54 cm²

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.

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:

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

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

30 cm²

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

24 cm²