Calculate Triangle Area: Finding Area with Sides 13cm, 15cm, and Height from Point D

Question

The triangle ABC has a perimeter measuring 42 cm.

AD = 12

AC = 15

AB = 13

Calculate the area of the triangle.

00:00 Calculate the area of triangle ABC

00:04 Substitute appropriate values according to the data

00:13 The perimeter of the triangle equals the sum of the sides

00:23 Substitute appropriate values according to the data

00:34 Calculate and solve to find BC

00:47 Isolate BC

00:58 This is the base length BC

01:02 Calculate the area of triangle ABC

01:05 Use the formula for calculating triangle area

01:08 (height(AD) multiplied by base(BC)) divided by 2

01:12 Substitute appropriate values

01:16 Calculate and solve

01:25 And this is the solution to the problem

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