Identify Pythagorean Triple

Since the triangle is right-angled, we use the Pythagorean theorem $a^2 + b^2 = c^2$. Given hypotenuse $c = 10$ and one side $a = 8$.

$8^2 + b^2 = 10^2 \implies 64 + b^2 = 100$

Solve for the missing side

Subtract the square of the given side from the hypotenuse square to find the other side $b$.

$b^2 = 100 - 64 = 36 \implies b = \sqrt{36} = 6$

Calculate Area

Use the formula for the area of a right-angled triangle, which is half the product of the two perpendicular sides (base and height).

$\text{Area} = \frac{1}{2} \times 6 \times 8 = 24 \text{ sq. units}$