Triangle Area Calculation: Find Area with Perimeter 26 and Height 6

Question

Calculate the area of the

triangle ABC given that its

perimeter equals 26.

00:00 Calculate the area of triangle ABC

00:03 The perimeter of the triangle equals the sum of its sides

00:12 Let's substitute appropriate values and calculate to find BC

00:23 Let's isolate BC

00:29 Now we have the length of base BC

00:38 Let's use the formula for calculating triangle area

00:41 (base(BC) times height(AE)) divided by 2

00:48 Let's substitute appropriate values and solve

01:01 And this is the solution to the problem

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:

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