Question

I need help finding the surface area of a right triangular prism. ​

Answer 1

Surface area of the right triangular prism = 180 m²

Explanation:

Surface area of the given right triangular prism = Surface area of triangular sides + Surface area of the rectangular surfaces

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

=
`(1)/(2)(AB)(AC)`

By applying Pythagoras theorem in ΔABC,

BC² = AB² + AC²

(13)² = 5² + (AC)²

AC² = 169 - 25

AC = 12 m

Therefore, area of the triangular sides =
`(1)/(2)(5)(12)` = 30 m²

Area of the rectangular side with dimensions 5m × 4m,

= 5 × 4

= 20 m²

Area of the rectangular side with dimensions 13m × 4m

= 13 × 4

= 52 m²

Area of the rectangular side with dimensions 12m × 4m

= 12 × 4

= 48 m²

Total surface area of the prism = 2(30) + 20 + 52 + 48

= 180 m²