# Area of the largest triangle that can be inscribed in a semi-circle of radius r units is

a. r² square units

b. 2r square units

c. 1/2 r² square units

d. r²/4 square units

**Solution:**

Given, radius of __semicircle__ is r units.

We have to find the area of the largest triangle that can be inscribed in semicircle.

Consider a semicircle.

AB is the __diameter__

AB = 2r units

Let the largest circle inscribed inside the semicircle is ABC.

So, the sides of the triangle AB = 2r

CD = r

We know that the angle in a semi circle is always equal to 90°

So, ∠ACB = 90°

Considering triangle ABC,

ACB is a right triangle with C at right angle.

__Area of triangle__ = (1/2) × base × height

Area of triangle ACB = (1/2) × AB × CD

= (1/2) × 2r × r

= r × r

= r² square units

Therefore, the area of a largest triangle that can be inscribed in a semicircle of radius r is r² square units.

**✦ Try This:** Find the area of the largest triangle that can be inscribed in a semicircle of radius 5 cm.

Given, radius of semicircle = 5 cm

We have to find the area of the largest triangle that can be inscribed in a semicircle.

Consider a semicircle

AC is the diameter

AC = 2(radius) = 2(5) = 10 cm

Let the triangle inscribed inside the semicircle be ABC

By the properties of circles,

∠ABC = 90°

Area of triangle = (1/2) × base × height

Area of triangle ABC = (1/2) × AC × CO

= (1/2) × 10 × 5

= 5(5)

= 25 square cm.

Therefore, the largest area of the triangle that can be inscribed in a semicircle of radius 5 cm is 25 square cm.

**☛ Also Check: **NCERT Solutions for Class 10 Maths Chapter 12

**NCERT Exemplar Class 10 Maths Exercise 11.1 Problem 4**

## Area of the largest triangle that can be inscribed in a semi-circle of radius r units is a. r² square units, b. 2r square units, c. 1/2 r² square units, d. r²/4 square units

**Summary:**

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is r² square units

**☛ Related Questions:**

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- The area of the circle that can be inscribed in a square of side 6 cm is a. 36π cm², b. 18π cm², c. . . . .

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