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

Question

Which of the following triangles have the same areas?

00:00 Determine which of the following triangles have the same area

00:03 Apply the formula for calculating the triangle area

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

00:14 Substitute in the relevant values and solve to find the area

00:20 This is the area of triangle IJK

00:26 Apply the same method and calculate the areas of the other triangles

00:34 Substitute in the height and base of the triangle EFG

00:53 This is the area of the triangle EFG

01:05 Substitute in the height and base of the triangle ABC

01:16 Substitute in the height and base of triangle ABC

01:25 This is the area of triangle ABC

01:32 This is the solution

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