Question

Find the area of the largest triangle that can be inscribed in a semicircle of radius 7cm.

Answer 1

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Answer 2

Answer:

The area of the largest triangle ABC inscribed in a semicircle of radius 7 cm is $49 cm^2$

To find:

The area of the largest triangle which is been inscribed in a semicircle of radius 7 cm

Solution:

$\angle A C B = 90 ^ { \circ }$

[Angle in a semi-circle = 90°]

Thus, Triangle ABC is a Right-Angled Triangle.

Thus Area of triangle ABC = Area of Triangle ADC + Area of Triangle BDC  

$= \left( \frac { 1 } { 2 } \times A D \times C D \right) + \left( \frac { 1 } { 2 } \times B D \times C D \right)$

$= \left( \frac { 1 } { 2 } \times 7 \times 7 \right) + \left( \frac { 1 } { 2 } \times 7 \times 7 \right) = \frac { 49 } { 2 } + \frac { 49 } { 2 } = 49 \mathrm { cm } ^ { 2 }$

Thus the area of the triangle ABC is $49 cm^2$.