The base and hypotenuse of a right-angled triangle are 9 cm and 41 cm respectively. What is the area of the triangle?

The base and hypotenuse of a right-angled triangle are 9 cm and 41 cm respectively.

As per the Pythagoras theorem, $$\left(hypotenuse\right)^2\ =\ \left(base\right)^2\ +\ \left(height\right)^2$$

$$\left(41\right)^2\ =\ \left(9\right)^2\ +\ \left(height\right)^2$$

$$1681=81\ +\ \left(height\right)^2$$

$$\ \left(height\right)^2 = 1681-81 = 1600$$

height = 40 cm

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

= $$\frac{1}{2}\times\ 9 \times\ 40$$

= $$ 9 \times\ 20$$

= 180 $$cm^{2}$$