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Surface Area of Prisms - Questions

Question 1
15150

Find the surface area of the following triangular prism, correct to the nearest \(\rm{m}^2\).

\(181~\text{m}^2\)

This triangular prism has 5 faces - Two identical triangles (front and back) and three different rectangles. The triangle is right-angled, whose two sides are 5m and 3m. So the third side (hypotenuse) is:
\[= \sqrt{5^2+3^2}= \sqrt{34}~\text{m}\]$$
\begin{aligned}
\text{Total Surface Area}&=\text{Area of two triangles + Area of 3 rectangles}\\
&=2\times \frac{1}{2}\times 3\times 5+12\times 5+3\times 12 + 12\times \sqrt{34}\\
&=15+60+36+12\times 5.83095\\
&=123+69.97\\
&=181~\text{m}^2
\end{aligned}
$$

Question 2
15151

Calculate the surface area of the net of the following prism 

\(213.2~\text{cm}^2\)

$$
\begin{aligned}
\text{Surface Area}&=2\times \frac{1}{2}\times (6\times 4)+11\times 4+11\times 6+11\times 7.2 \\
&=213.2~\text{cm}^2
\end{aligned}
$$

Question 3
15147

Calculate the surface area of the following cube

\(433.5~\text{m}^2\)

A cube has 6 identical faces in the shape of a square
$$
\begin{aligned}
\text{Surface area}&=6\times 8.5^2\\
&=433.5~\text{m}^2
\end{aligned}
$$

Question 4
15148

Calculate the surface area of the following rectangular prism 

\(8080~\text{cm}^2\)

A rectangular prism has 6 faces that are not all same. However, opposite faces such as the top and bottom are the same.

$$
\begin{aligned}
\text{Surface Area}&=\text{2 top bottom faces+2 end faces +2 side faces}\\
&=2\times 22\times 30+2\times 30\times 65 + 2\times 22\times 65\\
&=8080~\text{cm}^2
\end{aligned}
$$

Question 5
15149

Calculate the surface area of the following open rectangular prism (no top)

\(182.06~\text{m}^2\)

$$
\begin{aligned}
\text{Surface Area}&=\text{Bottom face+2 end faces +2 side faces}\\
&= 8.5\times 6.2+2\times 6.2\times 4.4+2\times 4.4\times 8.5 \\
&=182.06~\text{m}^2
\end{aligned}
$$

Question 6
112794

A rectangular prism has dimensions

  • width: \(DC=5 \text{ m}\)
  • length: \(CG=7 \text{ m}\)
  • height: \(AD=h \text{ m}\)

The surface area of the prism is \(106 \text{ m}^2\). Find the height of the prism. 

\(1.5 \text{ m}\)

Question 7
112795

A right triangular prism has dimensions

  • \(AC=13 \text{ cm}\)
  • \(AB=5 \text{ cm}\)
  • \(FC=16 \text{ cm}\)

Find the surface area of the prism. 

\(540 \text{ cm}^2\)

Question 8
112796

A trapezoidal prism has a surface area of \(128 \text{ cm}^2\). The dimensions of the prism are

  • \(AB=4 \text{ cm}\)
  • \(DC=10  \text{ cm}\)
  • \(CG=3 \text{ cm}\)
  • \(AD=BC=5 \text{ cm}\)

Find the height of the prism. 

\(4 \text{ cm}\)

Question 9
112797

The triangular prism has a surface area of \( 8 \sqrt{3}\). \(\Delta ABC\) is equilateral with sides \(BC=2\). Find the length of \(CF\)

\(\sqrt{3}\)

Question 10
112798

In the adjacent prism the dimensions are

  • \(DC=15\)
  • \(AD=18\)
  • \(BC=10\)
  • \(CG=12\)

Find the surface area of the prism. 

\(1140 \text{ u}^2\)