Question

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is
(a) r² sq units
(b)$\sf{\frac{1}{2}}$ r² sq units
(c) 2r² sq units
(d) √2 r²sq units​

Answer 1

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 x 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 = 1/2 × b × h formula for the area of a triangle

becomes

A = 1/2 x 2 x r x r because:

The base of the triangle is equal to 2 x r

The height of the triangle is equal to r

A = 1/2 x 2 xr xr becomes:

A = r²

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Answer 2

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

solution