Question

The area of the largest triangle inscribed in a semicircle of radius 8 is________
The circumference of a circle is 44 then the length of a side of a square inscribed in circle is_______

Answer 1

Answer:

Step-by-step explanation:

The area of a triangle is equal to the base times the height.

In a semi circle, the diameter is the base of the semi-circle.

This is equal to 2×r (r = the radius)

If the triangle is an isosceles triangle with an angle of 45  

∘

 at each end, then the height of the triangle is also a radius of the circle.

A =  

2

1

​  

×b×h formula for the area of a triangle becomes

A =  

2

1

​  

×2×r×r because:

The base of the triangle is equal to 2×r

The height of the triangle is equal to r

A =  

2

1

​  

×2×r×r becomes:

A = r  

2