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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