Question

find the total surface area of the prism. sa =? cm²

Explanation:

Step1: Calculate area of triangular bases

The area of a right - angled triangle is $A=\frac{1}{2}\times base\times height$. Here, base = 3 cm and height = 4 cm. So, $A_{triangle}=\frac{1}{2}\times3\times4 = 6$ $cm^{2}$. Since there are 2 triangular bases, the total area of the bases is $2\times6=12$ $cm^{2}$.

Step2: Calculate area of rectangular faces

There are 3 rectangular faces.
Face 1: with dimensions 3 cm and 7 cm, area $A_1 = 3\times7=21$ $cm^{2}$.
Face 2: with dimensions 4 cm and 7 cm, area $A_2 = 4\times7 = 28$ $cm^{2}$.
Face 3: with dimensions 5 cm and 7 cm, area $A_3=5\times7 = 35$ $cm^{2}$.
The total area of rectangular faces is $A_{rectangles}=21 + 28+35=84$ $cm^{2}$.

Step3: Calculate total surface area

The total surface area of the prism $SA$ is the sum of the area of the bases and the area of the rectangular faces. So, $SA=12 + 84=96$ $cm^{2}$.

Answer:

96