Question

jose builds a skateboard ramp in the shape of a right triangular prism. the net above shows the dimensions of each part of the ramp. what is the surface area, in square feet, of the ramp? show your thinking

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. For the triangular faces with base $b = 2.5$ ft and height $h=6$ ft, $A_{triangle}=\frac{1}{2}\times2.5\times6= 7.5$ square - feet. Since there are 2 triangular faces, the total area of triangular faces is $2\times7.5 = 15$ square - feet.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
Face 1: With dimensions $6.5$ ft and $4$ ft, $A_1=6.5\times4 = 26$ square - feet.
Face 2: With dimensions $6$ ft and $4$ ft, $A_2=6\times4 = 24$ square - feet.
Face 3: With dimensions $2.5$ ft and $4$ ft, $A_3=2.5\times4 = 10$ square - feet.
The total area of rectangular faces is $A_{rectangles}=26 + 24+10=60$ square - feet.

Step3: Calculate total surface area

The total surface area $A$ of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. So $A=15 + 60=75$ square - feet.

Answer:

75