Question

I need help finding the lateral and surface area of this prism and if the answer is too big it can be rounded to the nearest tenth

Answer 1

Lateral area = 647.1
`in^(2)`

Surface area = 1123.9
`in^(2)`

Explanation:

This is a triangular prism

Shape of base: Triangle

h = Perpendicular height = 9 in

Lateral area of triangular prism:

= (Perimeter of triangle) × h

= (20 in + 25 in + 26.9 in) × (9 in)

Lateral area = 647.1
`in^(2)`

Surface Area of triangular prism:

= 2(Area of triangle) + Lateral area

m = perpendicular height of triangle:

Area of triangle =
`(1)/(2)`×(base of triangle)×(m)

m is not provided, therefore area of triangle is calculated using Heron's formula:

Area of triangle =
`√(s(s-a)(s-b)(s-c))`

where s = semi-perimeter of the triangle =
`(a + b + c)/(2)`

=
`(20 + 25 + 26.9)/(2)`

= 35.95 in

∴ Area of triangle =
`√(35.95(35.95-20)(35.95 - 25)(35.95-26.9))`

=
`√(56822.7543)`
`in^(2)`

∴ Surface Area =[
`2(√(56822.7543)) + 647.10`]
`in^(2)`

= 1123.85
`in^(2)`

Surface Area = 1123.9
`in^(2)` (Rounded to the nearest tenth)