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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:

[tex]\frac{1}{2}[/tex] * base * height

[tex]\frac{1}{2}[/tex] * 8 * 6

24 cm²

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

Apply Pythagorean theorem

[tex]\\ \tt\hookrightarrow AN^2=10^2-6^2[/tex]

[tex]\\ \tt\hookrightarrow AN^2=8^2[/tex]

[tex]\\ \tt\hookrightarrow AN=8cm[/tex]

  • AB=2(8)=16cm

Area

[tex]\\ \tt\hookrightarrow \dfrac{1}{2}bh[/tex]

[tex]\\ \tt\hookrightarrow \dfrac{1}{2}(16)(10)=8(10)=80cm^2[/tex]

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

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