Question

what is the total surface area of the triangular prism? round to the nearest hundredth if necessary.

Explanation:

Step1: Calculate area of 2 triangular bases

The triangular base has base $8\ \text{m}$ and height $6\ \text{m}$. Area of one triangle is $\frac{1}{2} \times 8 \times 6 = 24\ \text{m}^2$. For two triangles:
$2 \times 24 = 48\ \text{m}^2$

Step2: Calculate lateral surface area

Lateral area is sum of areas of 3 rectangles. The rectangles have dimensions $(8 \times 22.25)$, $(6 \times 22.25)$, $(10 \times 22.25)$. Factor out $22.25$:
$22.25 \times (8 + 6 + 10) = 22.25 \times 24 = 534\ \text{m}^2$

Step3: Sum all areas for total surface area

Add the area of the two triangular bases and the lateral surface area:
$48 + 534 = 582\ \text{m}^2$

Answer:

$582$