At the base of the straight prism lies an isosceles trapezoid with a lateral side of 5 cm, and bases of 2 cm

| April 15, 2021 | education

At the base of the straight prism lies an isosceles trapezoid with a lateral side of 5 cm, and bases of 2 cm and 8 cm. The side edge of the prism is 6cm. Find the total surface area of the prism.

Let’s draw the HВ height at the base of the prism. Since an isosceles trapezoid lies at the base, the height BH divides the base of AD into two segments, the length of the smaller of which is equal to the half-difference of the lengths of its bases. AH = (AD – BC) / 2 = (8 – 2) / 2 = 3 cm.

From the right-angled triangle ABН, we determine the length of the leg BН according to the Pythagorean theorem.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 25 – 9 = 16.

BH = 4 cm.

Determine the area of ​​the base of the prism.

Sb = (ВС + АD) * ВН / 2 = (2 + 8) * 4/2 = 20 cm2.

Let us determine the area of ​​the lateral surface of the prism.

Sside = AA1 * Ravsd = 6 * (5 + 2 + 5 + 8) = 120 cm2.

Let’s define the total surface of the prism.

Sпов = 2 * Sсн + S side = 2 * 20 + 120 = 160 cm2.

Answer: The total surface area of ​​the prism is 160 cm2.



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