At the base of a straight prism is an isosceles triangle with a side side of 10 cm and a median drawn to the base, 8 cm

| March 9, 2021 | education

At the base of a straight prism is an isosceles triangle with a side side of 10 cm and a median drawn to the base, 8 cm. Calculate the volume of the prism if the diagonal of the larger side face is 13 cm.

In an isosceles triangle, which lies at the base of the prism, the median AH is also the height of the triangle. Let us define in a right-angled triangle ASN the leg CH according to the Pythagorean theorem. CH ^ 2 = AC ^ 2 – AB ^ 2 = 100 – 64 = 36.

CH = 6 cm, then the base BC = 2 * CH = 2 * 6 = 12 cm.

The base of BC is the large side of the base, then the diagonal of CB1 = 13 cm.

From the right-angled triangle CBB1, we define the leg BB1.

BB1 ^ 2 = CB1 ^ 2 – BC ^ 2 = 169 – 144 = 25.

BB1 = 5 cm.

Determine the area of ​​the base of the prism.

Sb = ВС * АН / 2 = 12 * 8/2 = 48 cm2.

Let’s define the volume of the prism.

V = Sbn * BB1 = 48 * 5 = 240 cm3.

Answer: The volume of the prism is 240 cm3.



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