Question

Find the area of a right-angled triangle, the radius of whose circumcircle measure 8 cm and the altitude drawn to the hypotenuse measures 6 cm.

Answer 1

Given: Radius = 8 cm
​Height = 6 cm
Area=?
In a right-angled triangle, the centre of the circumcircle is the mid-point of the hypotenuse.

$$\begin{gathered} \mathrm{Hypotenuse}=2\times (\mathrm{radius}\mathrm{of}\mathrm{circumcircle})\mathrm{for}\mathrm{a}\mathrm{right}\mathrm{triangle} \\ =2\times 8 \\ =16\mathrm{cm} \\ \text{So, h}\mathrm{ypotenuse}=16\mathrm{cm} \end{gathered}$$
Now, base = 16 cm and height = 6 cm

Area of the triangle =$\frac{1}{2}\times base\times height$

$$\begin{gathered} =\frac{1}{2}\times 16\times 6 \\ =48{\mathrm{cm}}^2 \end{gathered}$$