Question

ABC is the cross-section of the prism. Find the surface area and volume of the prism if AB = AC = 5 cm, BC = 6 cm and CR = 8 cm.

Answer 1

We have,

ABC is the cross-section of the prism.

If AB = AC = 5 cm, BC = 6 cm and CR = 8 cm

Now we know that,

The area of a triangle is `sqrt(s(s - a)(s - b)(s - c))`, where s is the semi-perimeter, a, b, c are the sides of a triangle

Then, in ΔABC

`s = (5 + 5 + 6)/2 = 8` cm

Then, area of the ΔABC = `sqrt(88 - 58 - 58 - 6)`

= 12 cm²

Now area of ΔABC = Area of ΔPQR

Then, area of ΔABC + Area of ΔPQR = 12 + 12 = 24 cm²

Now the area of a rectangle is (length)(breadth)

Then, area of the face ACRP = (5)(8) = 40 cm²

Area of the face ACRP = Area of the face ABQP

Then, area of face ACRP + Area of face ABQP = 40 + 40 = 80 cm²

And the area of the face BCRQ = (6)(8) = 48 cm²

The surface area of the prism = Area of ΔABC + Area of ΔPQR + Area of the face ACRP + Area of the face ABQP + Area of the face BCRQ

Therefore, the surface area of the prism = 12 + 12 + 40 + 40 + 48 = 152 cm²

And the volume of the prism = (Surface area of the cross-section ΔABC) × (Length)

= 12 × 8

= 96 cm³