At the base of the prism lies a rectangle, one of the sides of which is 6. The area of the diagonal section is 170 cm2.

| June 25, 2021 | education

At the base of the prism lies a rectangle, one of the sides of which is 6. The area of the diagonal section is 170 cm2. Find the surface area of the prism and not the volume, if not the height is 17cm.

The diagonal section of the prism is a rectangle АА1С1С, the area of ​​which is 170 cm2, and one of the sides is 17 cm, then AC = Ssection / АА1 = 170/17 = 10 cm.

In a right-angled triangle ACD, according to the Pythagorean theorem, we determine the length of the leg AD.

AD ^ 2 = AC ^ 2 – CD ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64.

AD = 8 cm.

Determine the area of ​​the base of the prism. Sbn = AD * AC = 8 * 6 = 48 cm2.

Let us determine the area of ​​the lateral surface of the prism. Sside = P * AA1, where P is the perimeter of the base of the prism. Side = 2 * (8 + 6) * 17 = 476 cm2.

Determine the total area of ​​the prism S floor = 2 * Sb + S side = 2 * 48 + 476 = 572 cm2.

Let’s define the volume of the prism.

V = Sbn * AA1 = 48 * 17 = 816 cm3.

Answer: The total area of ​​the prism is 572 cm2, the volume of the prism is 816 cm3.



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