Question

what is the surface area of this triangular prism? 16 cm 20 cm 20 cm 12 cm square centimeters submit work it out not feeling ready yet? these can help: area of triangles surface area of cubes and rect lesson: what is surface area?

Explanation:

Step1: Calculate area of triangular faces

The triangular faces have base $b = 12$ cm and height $h=16$ cm. The area of a triangle formula is $A_{\triangle}=\frac{1}{2}bh$. So, $A_{\triangle}=\frac{1}{2}\times12\times16 = 96$ square - cm. Since there are 2 triangular faces, the total area of triangular faces is $2\times96 = 192$ square - cm.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
Face 1: Dimensions $12\times20$, area $A_1 = 12\times20=240$ square - cm.
Face 2: Dimensions $16\times20$, area $A_2 = 16\times20 = 320$ square - cm.
Face 3: Dimensions $20\times20$, area $A_3 = 20\times20=400$ square - cm.
The total area of rectangular faces is $A_{rect}=240 + 320+400=960$ square - cm.

Step3: Calculate total surface area

The surface area of the triangular prism $A = A_{\triangle - total}+A_{rect - total}$. So, $A=192 + 960=1152$ square - cm.

Answer:

1152