Question

The area of the largest triangle that can be inscribed in a semicircle a of radius 21 cm (a) 221 sq.cm (b) 331 sq.cm (c) 441 sq.cm (d) 555 sq.cm​

Answer 1

Given:

radius of the semi-circle = 21cm

To find:

The area of the largest triangle that can be inscribed in the semicircle

Solution:

The largest triangle that can be inscribed in a semicircle has the diameter of the semicircle as its base and the radius as its perpendicular height.

So, according to the given statement, the radius of the given semicircle is 21cm.

We know that,

Diameter = 2(Radius)

So, the diameter of the semicircle can be evaluated as:

Diameter = 2×21

=42cm

Now, we can calculate the area of the triangle as:

Area=$\frac{1}{2}$×base×height

=$\frac{1}{2}$×42×21

=21×21

=441$cm^2$

Hence, the area of the largest triangle that can be inscribed in a semicircle of radius 21 cm is 441$cm^2$. (Option c)