Question

ami 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? (not drawn to scale) a 132 cm² b 176 cm² c 158 cm² d 152 cm²

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. Here, base = 6 cm and height = 4 cm. So $A_{triangle}=\frac{1}{2}\times6\times4 = 12$ $cm^{2}$. Since there are 2 triangular faces, the total area of triangular faces is $2\times12=24$ $cm^{2}$.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.

• One with dimensions 6 cm and 8 cm, its area $A_{1}=6\times8 = 48$ $cm^{2}$.
• One with dimensions 5 cm and 8 cm, its area $A_{2}=5\times8 = 40$ $cm^{2}$.
• One with dimensions 5 cm and 8 cm, its area $A_{3}=5\times8 = 40$ $cm^{2}$.

The total area of rectangular faces is $A_{rectangles}=48 + 40+40=128$ $cm^{2}$.

Step3: Calculate total surface - area

The surface area of the triangular prism $A = A_{triangles}+A_{rectangles}=24 + 128=152$ $cm^{2}$.

Answer:

D. $152$ $cm^{2}$