The perimeter of the base of a right prism, whose base is an equilateral triangle, is 24 cm. If its total surface area is (288+32 √3) cm 2, then its height is

Question

The perimeter of the base of a right prism, whose base is an equilateral triangle, is 24 cm. If its total surface area is (288+32 √3) cm 2, then its height is (A) 10 cm (B) 12 cm (C) 14 m (D) 14 cm

Tardigrade Admin · Accepted Answer

(i) LSA =288 cm 2. (ii) Take perimeter of the base as 3 a units and find a side (iii) LSA of prism is half the product of base, perimeter and slant height. (iv) TSA = LSA +2 (Area of the base). (v) Equate the given value to the above formula and find h.

Q. The perimeter of the base of a right prism, whose base is an equilateral triangle, is $24 c m$ . If its total surface area is $(288 + 323) c m^{2}$ , then its height is

10 cm

12 cm

14 m

14 cm

(i) $L S A = 288 c m^{2}$ .
(ii) Take perimeter of the base as $3 a$ units and find a side
(iii) LSA of prism is half the product of base, perimeter and slant height.
(iv) $TS A = L S A + 2$ (Area of the base).
(v) Equate the given value to the above formula and find $h$ .

Q. The perimeter of the base of a right prism, whose base is an equilateral triangle, is 24cm. If its total surface area is (288+323​)cm2, then its height is