Question

6 the base of a triangular prism is a right triangle with a hypotenuse of 74 mm and legs that are 70 mm and 24 mm. the height of the prism is 85 mm. what is its total surface area in square millimeters?

Explanation:

Step1: Calculate the area of the triangular base

The formula for the area of a right - triangle is \(A=\frac{1}{2}\times base\times height\). Here, the legs of the right - triangle (which act as base and height) are \(b = 24\space mm\) and \(h=70\space mm\).

$$A_{base}=\frac{1}{2}\times24\times70= 840\space mm^{2}$$

Step2: Calculate the lateral surface area

The lateral surface area of a triangular prism \(A_{lateral}=(a + b+ c)\times H\), where \(a = 24\space mm\), \(b = 70\space mm\), \(c = 74\space mm\) (the sides of the triangular base) and \(H = 85\space mm\) (height of the prism).
\((24 + 70+74)\times85=(168)\times85 = 14280\space mm^{2}\)

Step3: Calculate the total surface area

The total surface area of a triangular prism \(A_{total}=2A_{base}+A_{lateral}\)
Since \(A_{base}=840\space mm^{2}\) and \(A_{lateral}=14280\space mm^{2}\)

$$A_{total}=2\times840+14280$$

$$A_{total}=1680 + 14280=15960\space mm^{2}$$

Answer:

\(15960\space mm^{2}\)