Question

the triangular bases of a triangular prism have three congruent sides, each measuring 10 centimeters. the height of each of the triangular bases is approximately 8.7 centimeters. the height of the prism is 15 centimeters. what is the approximate surface area of the prism? 450 cm² 450 cm³ 537 cm² 537 cm³

Explanation:

Step1: Calculate base - area

The area of a triangular base $A_{base}=\frac{1}{2}\times base\times height$. Here, base = 10 cm and height = 8.7 cm. So $A_{base}=\frac{1}{2}\times10\times8.7 = 43.5$ $cm^{2}$.

Step2: Calculate lateral - face area

Each lateral face is a rectangle with dimensions 10 cm (base of the triangle) and 15 cm (height of the prism). The area of one lateral face $A_{lateral}=10\times15 = 150$ $cm^{2}$. Since there are 3 lateral faces, the total lateral - face area $A_{lateral - total}=3\times150=450$ $cm^{2}$.

Step3: Calculate total surface area

The total surface area of the triangular prism $A = 2A_{base}+A_{lateral - total}$. Substitute $A_{base}=43.5$ $cm^{2}$ and $A_{lateral - total}=450$ $cm^{2}$ into the formula. $A = 2\times43.5+450=87 + 450=537$ $cm^{2}$.

Answer:

$537$ $cm^{2}$