Right Triangle Area Calculation: 36cm Perimeter with Given Side Lengths

Question

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

Solution Steps

00:00 Calculate the area of triangle ABD

00:03 Substitute appropriate values according to the given data

00:15 The side (BD) equals the sum of its parts (BC+CD)

00:19 Substitute appropriate values according to the given data

00:24 And this is the length of the base (BD)

00:29 The perimeter of the triangle equals the sum of its sides

00:38 Substitute appropriate values

00:50 Let's solve to get DA

00:53 Let's isolate DA

01:01 Calculate and solve

01:05 And this is the height length (DA)

01:11 Now we want to calculate the area of triangle ABD

01:14 We'll use the formula for calculating triangle area

01:17 (Height(AD) multiplied by base(BD)) divided by 2

01:21 Substitute appropriate values

01:25 Calculate and solve

01:33 And this is the solution to the question

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

Related Subjects

Question Types

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