Question

aaron is making building blocks. the blocks are shaped like triangular prisms with two triangular faces and three rectangular faces. what is the surface area of each block? a 136 cm² b 124 cm² c 106 cm² d 110 cm²

Explanation:

Step1: Calculate the area of the triangular faces

The formula for the area of a triangle is \(A = \frac{1}{2}bh\). Here, \(b = 4\space cm\) and \(h=3.5\space cm\).
For two triangular faces: \(2\times\frac{1}{2}\times4\times3.5= 14\space cm^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• One with dimensions \(4\times8\): \(A_1=4\times8 = 32\space cm^{2}\)
• One with dimensions \(4\times8\): \(A_2 = 4\times8=32\space cm^{2}\)
• One with dimensions \(4\times8\): \(A_3=4\times8 = 32\space cm^{2}\)

The sum of the areas of the rectangular faces is \(32 + 32+32=96\space cm^{2}\)

Step3: Calculate the total surface area

The total surface area \(S\) of the triangular prism is the sum of the areas of the triangular and rectangular faces.
\(S=14 + 96=110\space cm^{2}\)

Answer:

D. \(110\space cm^{2}\)