It is known that the perimeter of a triangle (P) is equal to the sum of the lengths of its sides:
P = a + b + c, where a, b, c are the sides of the triangle.
Since the sides are equal in an isosceles triangle, the perimeter of such a triangle will be: P = 2a + c.
If you know the perimeter and side of the triangle, then you can find the third side by the formula:
c = P – 2a,
c = 16 – 2 * 5 = 6 cm.
Let’s calculate the height of the triangle:
h ^ 2 = 5 ^ 2 – 3 ^ 2,
h ^ 2 = 25 – 9,
h ^ 2 = 16,
h = 4.
Let’s calculate the area of the rectangle:
S = 1/2 * c * h,
S = 1/2 * 6 * 4 = 12.
Answer: The area of a given isosceles triangle is 12.
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