Question

8.5 cm 6.5 cm 2.25 cm Which measurement is closest to the surface area of the triangular prism in square centimeters?

Answer 1

This problem provides the faces of a triangular prism, and we need to calculate the surface area.

The surface area of the prism is equal to the sum of the area of all individual faces. Three faces are rectangles, while two are triangles.

The area of a rectangle can be found by using the following expression:

`A_(rectangle)=length*width`

While the area of a triangle can be found by using the following expression:

`A_(triangle)=(base*height)/(2)`

Two rectangles are equal, with measurements 2.25 cm by 8.5 cm, one rectangle has a measurement of 6.5 cm by 2.5 cm, and the two triangles are equal with a base equal to 6.5 cm and a height of 8.5 cm, therefore we have:

`\begin{gathered} A_(rectangle)1=2.25\cdot8.5=19.125\text{ cm}\\ \\ A_(rectangle)2=6.5\cdot2.25=14.625\text{ cm}\\ \\ A_(triangle)=(6.5\cdot8.5)/(2)=27.625\text{ cm}\\ \\ \end{gathered}`

And the total area is:

`\begin{gathered} A_(total)=2\cdot A_(rectangle)1+A_(rectangle)2+2\cdot A_(triangle) \\ A_(total)=2\cdot19.125+14.625+2\cdot27.625 \\ A_(total)=108.125\text{ square centimeters} \end{gathered}`

The surface area of the prism is approximately 108 square centimeters.