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

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KollegeApply · Accepted Answer

Area of the largest triangle that can be inscribed in a semi-circle of radius r units is r2 sq.units. Explanation: The largest triangle that can be inscribed in a semi-circle of radius r units is the triangle having its base as the diameter of the semi-circle and the two other sides are taken by considering a point C on the circumference of the semi-circle and joining it by the endpoints of diameter A and B. $\therefore$ $\angle$C = $90^\circ$ ...(By the properties of circle) So, ΔABC is right-angled triangle with base as diameter AB of the circle and height be CD. Height of the triangle = r $\therefore$ Area of largest ΔABC = $\frac{1}{2}$ xx "Base" xx "Height" = $\frac{1}{2}$ xx "AB" xx "CD" = $\frac{1}{2}$ xx 2"r" xx "r" = r2 sq.units [Solution diagram: 64109_solution_1.png]

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