A isosceles triangular prism has a height of $15 c m$ $15 cm$ , the perimeter of the base is $32 c m$ $32 cm$ and the base of the triangle is $\frac{6}{5}$ $6/5$ the side. Calculate the surface area of the prism?

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Answer 1 · 2018-06-02T10:28:22

Surface area of prism $A_{T} = 576 c m^{2}$ $color(maroon)(A_T = 576 cm^2$

Total Surface Area of prism = 2 * base Area + lateral surface area of the prism

Given $h = 15 c m, p = 32 c m, b = c, a = (\frac{6}{5}) b$ $h = 15cm, p = 32cm, b = c, a = (6/5)b$

$a + b + c = p$ $a + b + c = p$

$(\frac{6}{5}) b + b + b = 32$ $(6/5)b + b + b = 32$

$16 b = 32 \cdot 5, b = 10 c m$ $16b = 32*5, b = 10cm$

$a = (\frac{6}{5}) b = (\frac{6}{5}) \cdot 10 = 12 c m$ $a = (6/5)b = (6/5)*10 = 12cm$

Semi perimeter $s = \frac{a + b + c}{2} = \frac{12 + 10 + 10}{2} = 16 c m$ $s = (a + b + c)/2 = (12+10+10)/2 = 16cm$

Area of base triangle $A_{t} = \sqrt{s (s - a) (s - b) (s - c)}$ $A_t = sqrt( s (s-a) (s-b) (s-c))$

$A_{t} = \sqrt{16 \cdot (16 - 12) (16 - 10) (16 - 10)} = 48 c m^{2}$ $A_t = sqrt(16*(16-12)(16-10)(16-10)) = 48 cm^2$

Lateral Surface Area of prism $A_{l} = 2 \cdot b \cdot h + a \cdot h$ $A_l = 2 * b * h + a * h$

$A_{l} = 2 \cdot 10 \cdot 15 + 12 \cdot 15 = 480 c m^{2}$ $A_l = 2 * 10 * 15 + 12*15 = 480 cm^2$

$T S A = A_{T} = 2 \cdot A_{t} + A_{l} = 2 \cdot 48 + 480 = 576 c m^{2}$ $color(maroon)(T S A = A_T = 2 * A_t + A_l = 2 * 48 + 480 = 576 cm^2$

A isosceles triangular prism has a height of 15 cm15cm15 cm, the perimeter of the base is 32 cm32cm32 cm and the base of the triangle is 6/5656/5 the side. Calculate the surface area of the prism?