CUET UG 2025 — General Test Geometry

2025mcqmedium

The area of the right-angled isosceles triangle having hypotenuse A cm is:

Official previous-year question

Held on 2 Jun 2025 · Verified 13 Jul 2026.

Options

A
$\frac{A^2}{2}$
B
$\frac{A^2}{8}$
C
$\frac{A^2}{4}$
D
$\frac{A^2}{3}$

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Solution

In a right-angled isosceles triangle, two sides are equal in length and meet at a 90° angle.

Let the two equal sides each have length $a$ cm.

The hypotenuse is given as $A$ cm.

By the Pythagorean theorem:

$a^2 + a^2 = A^2$

$2a^2 = A^2$

$a^2 = \dfrac{A^2}{2}$

The two equal sides are perpendicular to each other, so they serve as the base and height of the triangle.

Area $= \dfrac{1}{2} \times \text{base} \times \text{height}$

Area $= \dfrac{1}{2} \times a \times a$

Area $= \dfrac{1}{2} \times a^2$

Substituting $a^2 = \dfrac{A^2}{2}$ :

Area $= \dfrac{1}{2} \times \dfrac{A^2}{2}$

Area $= \dfrac{A^2}{4}$

Therefore, the area of the triangle is $\dfrac{A^2}{4}$ square cm.

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Solution

In a right-angled isosceles triangle, two sides are equal in length and meet at a 90° angle.

Let the two equal sides each have length $a$ cm.

The hypotenuse is given as $A$ cm.

By the Pythagorean theorem:

$a^2 + a^2 = A^2$

$2a^2 = A^2$

$a^2 = \dfrac{A^2}{2}$

The two equal sides are perpendicular to each other, so they serve as the base and height of the triangle.

Area $= \dfrac{1}{2} \times \text{base} \times \text{height}$

Area $= \dfrac{1}{2} \times a \times a$

Area $= \dfrac{1}{2} \times a^2$

Substituting $a^2 = \dfrac{A^2}{2}$ :

Area $= \dfrac{1}{2} \times \dfrac{A^2}{2}$

Area $= \dfrac{A^2}{4}$

Therefore, the area of the triangle is $\dfrac{A^2}{4}$ square cm.

CUET UG 2025 — General Test Geometry

Options

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Solution

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CUET UG 2025 — General Test Geometry

Options

Did you get this right?

Solution

Your note

CUET UG Geometry in other years

More CUET UG Geometry questions

Other General Test topics for CUET UG

General Knowledge

Logical Reasoning

Arithmetic

Quantitative Reasoning

Current Affairs

Keep practicing Geometry