Find the area of the prism. ABCD and A₁B₁C₁D₁ are equal trapezoids

| September 26, 2021 | education

Find the area of the prism. ABCD and A₁B₁C₁D₁ are equal trapezoids, BC = 10 cm, AD = 22 cm. The sides are squares with a side of 10 cm.

Since the sides of the prism are squares with the side of the prism, its height is АА1 = 10 cm.

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

Sside = Ravsd * AA1, where Ravsd is the perimeter of the trapezium at the base of the prism.

Ravsd = 10 +10 + 10 + 22 = 52 cm.

Side = 52 * 10 = 520 cm2.

At the base of the trapezoid, we will build the height BH. Since the sides of the prism are squares, the trapezoid ABCD is isosceles, AB = CD = 10 cm.

The BH height divides the base of the trapezium into two segments, the length of the smaller of which is equal to the half-difference of the lengths of the bases. AH = (AD – BC) / 2 = (22 – 10) / 2 = 6 cm.

From the right-angled triangle ABH, according to the Pythagorean theorem, BH ^ 2 = AB ^ 2 – AH ^ 2 = 100 – 36 = 64. BH = 8 cm.

Then Sbn = (ВС + АD) * ВН / 2 = (10 + 22) * 8/2 = 128 cm2.

Sprism = 2 * Sb + S side = 2 * 128 + 520 = 776 cm2.

Answer: The area of ​​the prism is 776 cm2.



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