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

Answer:

area of ΔABC = 48 cm²

Step-by-step 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:

$\frac{1}{2}$ * base * height

$\frac{1}{2}$ * 8 * 6

24 cm²

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

Answer 2

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

$\\ \tt\hookrightarrow \dfrac{1}{2}bh$

$\\ \tt\hookrightarrow \dfrac{1}{2}(16)(10)=8(10)=80cm^2$

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