Triangle Area Comparison: Analyzing Three 5-12-13 Configurations

Question

Which of the following triangles have the same areas?

00:00 Which triangles have the same area?

00:03 Let's use the formula for calculating triangle area

00:07 (height multiplied by base) divided by 2

00:14 Let's substitute appropriate values and solve to find the area

00:20 This is the area of triangle IJK

00:26 Let's use the same method and calculate the areas of the other triangles

00:34 Let's substitute the height and base of triangle EFG

00:53 This is the area of triangle EFG

01:05 Let's substitute the height and base of triangle ABC

01:16 Let's substitute the height and base of triangle ABC

01:25 This is the area of triangle ABC

01:32 And this is the solution to the question

We calculate the area of triangle ABC:

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

We calculate the area of triangle EFG:

$\frac{6\times10}{2}=\frac{60}{2}=30$

We calculate the area of triangle JIK:

$\frac{6\times5}{2}=\frac{30}{2}=15$

Therefore, the triangles that have the same areas are ABC and EFG.

EFG and ABC