Question

what is the surface area of this triangular prism? 20 ft. 16 ft. 20 ft. 24 ft. 8 ft. square feet

Explanation:

Step1: Calculate area of triangular bases

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 24$ ft and $h=16$ ft. So, $A_{base}=\frac{1}{2}\times24\times16= 192$ square - feet.

Step2: Calculate area of first rectangular face

The first rectangular face has dimensions 20 ft (slant - height) and 8 ft. So, $A_{1}=20\times8 = 160$ square - feet.

Step3: Calculate area of second rectangular face

The second rectangular face has dimensions 20 ft (slant - height) and 8 ft. So, $A_{2}=20\times8 = 160$ square - feet.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions 24 ft and 8 ft. So, $A_{3}=24\times8=192$ square - feet.

Step5: Calculate total surface area

The total surface area $A_{total}=2A_{base}+A_{1}+A_{2}+A_{3}$. Substitute the values: $A_{total}=2\times192 + 160+160+192$.
$A_{total}=384+160 + 160+192=896$ square - feet.

Answer:

896