# At the base of the straight prism lies an isosceles right-angled triangle with leg 13.

July 22, 2021 | education

| **At the base of the straight prism lies an isosceles right-angled triangle with leg 13. The lateral edge is 6. Find the area of the lateral surface.**

At the base of the pyramid lies an isosceles, right-angled triangle, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AC ^ 2 + BC ^ 2 = 169 + 169 = 338.

AC = 13 * √2 cm.

Let’s define the perimeter of the triangle ABC.

Ravs = (AB + BC + AC) = 13 * √2 + 13 + 13 = 26 + 13 * √2 = 13 * (2 + √2) cm.

Since the prism is straight, its lateral faces are rectangles, then Sside = Ravs * AA1 = 13 * (2 + √2) * 6 = 78 * (2 + √2) cm2.

Answer: The lateral surface area is 78 * (2 + √2) cm2.

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