Answer:
Jess is building a skateboarding ramp in the shape of a triangular prism with the dimensions shown. If Jess wants to cover all faces of the ramp with plywood, how much plywood will he need?
96 square feet 144 square feet
156 square feet 168 square feet
Plywood needed = 156 square feet
Step-by-step explanation:
Given:
Height of the triangular prism = 12 feet
Perimeter of its base = 3+4+5 = 12 feet
We have to find the surface area of the triangular prism so that we can identify how much plywood will be needed to cover its faces.
Formula :
SA = 2(Area of the triangles) + (Perimeter of its base)(Height)
Or
SA = 2(area of the triangles) + area of the 3 rectangles with different width but a common height.
⇒ Surface area of the prism:
⇒ [tex]2(ar\ \triangle)+ p(\triangle)(H)[/tex]
⇒ [tex]2\times \frac{(3\times 4)}{2} +(3+4+5)(12)[/tex] ...area of [tex]\triangle[/tex] = 1/2*base*height
⇒ [tex]12+12(12)[/tex] ...perimeter of [tex]\triangle[/tex] is sum of all sides.
⇒ [tex]12+144[/tex]
⇒ [tex]156[/tex] square feet.
So,
Jess will need 156 square feet of plywood to cover all faces of the ramp.
