The base of a straight prism is a right-angled triangle with a leg 8cm. and with an acute angle of 45 degrees.

| August 9, 2021 | education

The base of a straight prism is a right-angled triangle with a leg 8cm. and with an acute angle of 45 degrees. The volume of the prism is 320 cm3. Find the total surface area of the prism.

According to the condition of the problem, the acute angle in a right-angled triangle is 45 degrees, therefore this triangle is isosceles and its legs are equal to each other.

Since both legs of the triangle are 8 cm, the area of the triangle is:

S = 8 * 8/2 = 32 cm².

As you know, the volume of a prism is equal to the product of the area of its base by the height, which means that the height of this prism is equal to:

h = 320: 32 = 10 cm.

Knowing what the height of the prism is, we can find the total area of its surface:

S = 32 * 2 + 3 * 8 * 10 = 64 + 240 = 304 cm².



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