The side of an isosceles triangle is √61 and the height of the triangle drawn to the base is 5

The side of an isosceles triangle is √61 and the height of the triangle drawn to the base is 5, calculate the area of this triangle.

Let us introduce the notation. Given by the condition triangle ABC, AC – base, AB = BC = √61, BH = 5 – height.
In the right-angled triangle ABN we find the leg AN (according to the Pythagorean theorem):
AH = √ (AB² – BH²) = √ (61 – 25) = √36 = 6.
AC = 2 * AH = 2 * 6 = 12.
We find the area of the triangle ABC:
S ABC = 1/2 * AC * BH = 1/2 * 12 * 5 = 30.
Answer: The area of the triangle is 30.