The area of the right-angled isosceles triangle having hypotenuse \(A\) cm is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{A^2}{4}\)
In a right-angled isosceles triangle, the two equal sides are the sides containing the right angle, so one is the base and the other the height.
By Pythagoras’ theorem, \(a^2+a^2=A^2\), so \(\displaystyle a^2=\frac{A^2}{2}\)
Area \(\displaystyle =\frac{1}{2}\times a\times a=\frac{a^2}{2}=\frac{A^2}{4}\)