Find the height of a rectangular prism at the base of which is an isosceles trapezoid with parallel

Find the height of a rectangular prism at the base of which is an isosceles trapezoid with parallel sides of 8 and 18 cm and a side side of 13 cm if its volume is 780 cm3.

In a trapezoid, the larger base is equal to the sum of the lengths of the smaller base and the projections of the two lateral sides. Since the trapezoid given by the condition is isosceles, its lateral sides are equal, therefore, their projections are also equal. We find the length of the projection of the lateral side as half the difference in the lengths of the bases: (18 – 8) / 2 = 10/2 = 5 cm.

From the right-angled triangle formed by the lateral side, its projection and the height of the trapezoid, according to the Pythagorean theorem, we can find the height of the trapezoid:

h ^ 2 = 13 ^ 2 – 5 ^ 2 = 169 – 25 = 144 = 122;

h = 12 cm.

The area of ​​the trapezium lying at the base of this prism is found as the product of the half-sum of the bases and the height of the trapezoid:

Sbn = Str = 12 * (18 + 8) / 2 = 12 * 13 = 156 cm2.

The volume of the prism is equal to the product of the base area and the height of the prism. Knowing the base area and volume of the prism, we find its height:

V = Sbas * H;

H = V / Sb = 780/156 = 5 cm.