Question

In the figure below, angles ACB and ANC are right-angles. What is the 10cm area of AABC?

A 24 cm²
B 37.5cm²
C 40cm²
D 75 cm²​

Answer 1

Apply Pythagorean theorem

`\\ \tt\hookrightarrow AN^2=10^2-6^2`

`\\ \tt\hookrightarrow AN^2=8^2`

`\\ \tt\hookrightarrow AN=8cm`

• AB=2(8)=16cm

Area

`\\ \tt\hookrightarrow (1)/(2)bh`

`\\ \tt\hookrightarrow (1)/(2)(16)(10)=8(10)=80cm^2`

Required area:-80/2=40cm^2

Answer 2

area of ΔABC = 48 cm²

Explanation:

We have been provided with height of 6 cm and have to find base.

using Pythagoras theorem:

a² + b² = c²

a² + 6² = 10²

a² = 100 -36

a² = 64

a = √64

a = 8

Area of both triangles:

`(1)/(2)` * base * height

`(1)/(2)` * 8 * 6

24 cm²

area of both triangles: 24 cm² * 2 = 48 cm²