Find the area of the largest triangle that can be inscribed in a semi-circle of radius r units. [CBSE 2015]

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Solution

Radius of the semi circle r units

When a largest triangle inscribed in a semicircle, then base = r + r = 2r units

Thus, Area of triangle is given by
$\frac{1}{2} \times base \times height = \frac{1}{2} \times (2 r) \times r = r^{2} square units$

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Q. What is the area of the largest triangle that can be inscribed in a semi-circle of radius 'r'?

The area of the largest triangle that can be inscribed in a semi-circle of radius $r$ is
(a) $2 r^{2}$ sq. units
(b) $r^{2}$ sq. units
(c) $\frac{1}{2} r^{2}$ sq. units
(d) $\sqrt{2} r^{2}$ sq. units

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Find the area of the largest triangle that can be inscribed in a semi-circle of radius r units. [CBSE 2015]

Radius of the semi circle r units When a largest triangle inscribed in a semicircle, then base = r + r = 2r units Thus, Area of triangle is given by 12×base×height=12×2r×r=r2 square units

Radius of the semi circle r units

When a largest triangle inscribed in a semicircle, then base = r + r = 2r units

Thus, Area of triangle is given by
$\frac{1}{2} \times base \times height = \frac{1}{2} \times (2 r) \times r = r^{2} square units$