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

Answer

Explanation:

Step1: Calculate area of triangular bases

The area formula for a triangle is $A=\frac{1}{2}bh$. Here, $b = 6$ cm and $h=4$ cm. So, $A_{base}=\frac{1}{2}\times6\times4= 12$ $cm^{2}$. Since there are 2 triangular bases, the total area of the bases is $2\times12 = 24$ $cm^{2}$.

Step2: Calculate area of rectangular - side 1

One rectangular face has dimensions $6$ cm (base - length of the triangle) and $8$ cm. So, $A_{rect1}=6\times8 = 48$ $cm^{2}$.

Step3: Calculate area of rectangular - side 2

The other two rectangular faces have dimensions $5$ cm (slant - length of the triangle) and $8$ cm. Each has an area of $A_{rect2}=5\times8=40$ $cm^{2}$, and the total area of these two faces is $2\times40 = 80$ $cm^{2}$.

Step4: Calculate total surface area

The total surface area $SA$ of the prism is the sum of the areas of the bases and the lateral faces. So, $SA=24 + 48+80=152$ $cm^{2}$.

Answer:

$152$