# What is the area of a right-angled isosceles triangle if its hypotenuse is 3√2 cm?

September 28, 2021 | education

| The area of a right-angled triangle is found by the formula:

S = 1/2 * a * b,

where a and b are legs.

Since, according to the condition, an isosceles right-angled triangle is given, its legs are equal, which means that the area of such a triangle is equal to:

S = 1/2 * a * a = (a ^ 2) / 2.

Let us find the length of the leg of the triangle according to the Pythagorean theorem:

a ^ 2 + b ^ 2 = c ^ 2;

a ^ 2 + a ^ 2 = (3√2) ^ 2;

2 * a ^ 2 = 3 * 2;

2 * a ^ 2 = 6;

a ^ 2 = 6/2;

a ^ 2 = 3;

a = √3 cm.

Find the area of a right-angled isosceles triangle:

S = ((√3) ^ 2) / 2 = 3/2 = 1.5 (cm ^ 2).

Answer: S = 1.5 (cm ^ 2).

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