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. 10 cm 15 cm what is the approximate surface area of the prism? 450 cm² 450 cm³ 537 cm² 537 cm³

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 10\) cm and \(h=8.7\) cm.
\(A_{base}=\frac{1}{2}\times10\times8.7 = 43.5\) \(cm^{2}\). Since there are \(2\) triangular bases, \(A_{total - bases}=2\times43.5=87\) \(cm^{2}\).

Step2: Calculate the area of the rectangular faces

The prism has \(3\) congruent rectangular faces. The formula for the area of a rectangle is \(A = lw\). Here, \(l = 15\) cm (height of the prism) and \(w = 10\) cm (side of the triangular base).
\(A_{rect - face}=15\times10 = 150\) \(cm^{2}\). Since there are \(3\) rectangular faces, \(A_{total - rect}=3\times150 = 450\) \(cm^{2}\).

Step3: Calculate the total surface area

The total surface area \(A\) of the triangular prism is the sum of the areas of the triangular bases and the rectangular faces.
\(A=A_{total - bases}+A_{total - rect}\)
\(A=87 + 450=537\) \(cm^{2}\).

Answer:

\(537\ cm^{2}\) (the third option)