Question

34 in.

16 in.
22 in.
Lateral Surface Area =
in squared
Total Surface Area =
in squared
Volume =
in cubed

Answer 1

Explanation:

Lateral surface area of the triangular prism = Perimeter of the triangular base × Height

By applying Pythagoras theorem in ΔABC,

AC² = AB² + BC²

(34)² = (16)² + BC²

BC =
`√(1156-256)`

=
`√(900)`

= 30 in.

Perimeter of the triangular base = AB + BC + AC

= 16 + 30 + 34

= 80 in

Lateral surface area = 80 × 22

= 1760 in²

Total Surface area = Lateral surface area + 2(Surface area of the triangular base)

Surface area of the triangular base =
`(1)/(2)(\text{Base})(\text{Height})`

=
`(1)/(2)(30)(16)`

= 240 in²

Total surface area = 1760 + 2(240)

= 1760 + 480

= 2240 in²

Volume = Area of the triangular base × Height

= 240 × 20

= 4800 in³