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

The triangle ABC has a perimeter measuring 42 cm.

AD = 12

AC = 15

AB = 13

Calculate the area of the triangle.

131313151515121212AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the area of the triangle ABC
00:04 Substitute in the relevant values according to the data
00:13 The perimeter of the triangle equals the sum of the sides
00:23 Substitute in the relevant 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 the triangle ABC
01:05 Apply the formula for calculating the area of the triangle
01:08 (height(AD) x base (BC)) divided by 2
01:12 Substitute in the relevant values
01:16 Calculate and solve
01:25 This is the solution

Step-by-step written solution

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1

Understand the problem

The triangle ABC has a perimeter measuring 42 cm.

AD = 12

AC = 15

AB = 13

Calculate the area of the triangle.

131313151515121212AAABBBCCCDDD

2

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=42−28=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

3

Final Answer

84 cm²

Practice Quiz

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Angle A is equal to 30°.
Angle B is equal to 60°.
Angle C is equal to 90°.

Can these angles form a triangle?

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