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? 132 cm² 158 cm² 176 cm² 152 cm²

Explanation:

Step1: Calculate area of triangular faces

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 6$ cm and $h=4$ cm. So the area of one - triangular face is $A_{triangle}=\frac{1}{2}\times6\times4 = 12$ $cm^{2}$. The total area of the two triangular faces is $2\times12=24$ $cm^{2}$.

Step2: Calculate area of first rectangular face

One rectangular face has dimensions $6$ cm (base of the triangle) and $8$ cm. Its area $A_{1}=6\times8 = 48$ $cm^{2}$.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions $5$ cm and $8$ cm. Its area $A_{2}=5\times8 = 40$ $cm^{2}$.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions $5$ cm and $8$ cm. Its area $A_{3}=5\times8 = 40$ $cm^{2}$.

Step5: Calculate total surface area

The total surface area $A = A_{triangles}+A_{1}+A_{2}+A_{3}=24 + 48+40 + 40=152$ $cm^{2}$.

Answer:

$152$ $cm^{2}$