Question

Calculate the surface area of a triangular prism 10.8cm long and having a triangle bar face of dimensions 8.8cm by 5.7cm by 6.8cm​

Answer 1

268.8

Explanation:

Let the sides of the base triangle be:

a = 8.8 cm

b = 5.7 cm

c = 6.8 cm

Let h be the length

h = 10.8 cm

The surface area is given by:

`SA = (a + b + c)*l + 2√( s(s - a)(s - b)(s - c))`

Where

`s = (a + b + c)/(2) \\\\= (8.8 + 5.7 + 6.8)/(2) \\\\=(21.3)/(2) \\\\= 10.65`

`SA = (a + b + c)*l + 2√( s(s - a)(s - b)(s - c))\\\\= (8.8 + 5.7 + 6.8)*10.8 + 2√( 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8))\\\\= 21.3*10.8 +2√( 10.65(10.65 - 8.8)(10.65 - 5.7)(10.65 - 6.8))\\\\=230.04 + 2√( 10.65(1.85)(4.95)(3.85))\\\\=230.04 + 2√( 375.48)\\\\= 230.04 + 2*19.38\\\\=230.04 +38.76\\\\=268.8`