Question

9. What is the area of the region left if three equilateral triangles are cut off
from a semi circle of radius 4cm? *​

Answer 1

Answer:

$4.35 cm^2$

Step-by-step explanation:

For the equilateral triangle in a semicircle of radius 4cm.

Side Lengths =4cm

Angles =60 degrees

$\text{Area of a Triangle}=\frac{1}{2}ab\sin \theta$

Therefore, the area of one equilateral triangle

$=\frac{1}{2}*4*4*\sin 60^\circ$

Area of the three equilateral triangle

$=3*\frac{1}{2}*4*4*\sin 60^\circ\\=20.7846 cm^2$

Area of the semicircle

$=0.5 \times \pir^2\\=0.5 \times \pi * 4^2\\=25.1327 cm^2$

Therefore, the area left over =Area of Semicircle -Area of Triangles

=25.1327-20.7846

=$4.35 cm^2$