Each side edge of the pyramid is 13 cm. The base of the pyramid is a right-angled triangle

| March 2, 2021 | education

Each side edge of the pyramid is 13 cm. The base of the pyramid is a right-angled triangle with legs 6 cm and 8 cm. Find the surface area of the pyramid.

Let us determine the length of the hypotenuse AB of the base of the pyramid.

AB ^ 2 = BC ^ 2 + AC ^ 2 = 64 + 36 = 100.

AB = 10 cm.

Determine the area of ​​the base of the pyramid.

Sbn = АС * ВС / 2 = 6 * 8/2 = 24 cm2.

The areas of the side faces are determined by Heron’s theorem.

Let’s define the perimeters of the side faces.

Dist = 13 + 13 + 6 = 32 cm, then p (asd) = 32/2 = 16 cm.

Then Sacd = √16 * 3 * 3 * 10 = √1440 = 12 * √10 cm2.

Rvsd = 13 + 13 + 8 = 34 cm, then p (asd) = 34/2 = 17 cm.

Then Svsd = √17 * 4 * 4 * 9 = √2448 = 12 * √17 cm2.

Ravd = 13 + 13 + 10 = 36 cm, then p (asd) = 36/2 = 18 cm.

Then Savd = √18 * 5 * 5 * 8 = √3600 = 60 cm2.

Spov = Smax + Sasd + Svsd + Savd = 24 + 12 * √10 + 12 * √17 + 60 = 12 * (7 + √10 + √17) cm2.

Answer: The surface area is 12 * (7 + √10 + √17) cm2.



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