Question

Calculate the surface area (in ${cm}^{2}$ ) of the following prisms. And, complete the Venn diagram below.

Accepted Answer

Prism (i),

The diagram shows a rectangular prism.

The surface area of a rectangular prism is the total area of all six faces.

Surface area of a rectangular prism $= 2 (l b \times b h \times l h)$ , where, $l$ is length, $b$ is breadth and $h$ is height.

So, surface area of the given prism $= 2 (6 \times 2.5 + 2.5 \times 4.2 + 4.2 \times 6)$

$= 2 (15 + 10.5 + 25.2) = 101.4 {cm}^{2}$

Prism (ii),

The diagram shows a combination of two rectangular prisms.

The surface area of a prism can be found by adding together the area of each face.

So, surface area of the given prism $= [(6 \times 5) + (4 \times 5) + 2 (6 \times 2.5) + 2 (5 \times 2.5)] + [(2 \times 5) + 2 (2 \times 2) + 2 (5 \times 2)]$

$= 105 + 38 = 143 {cm}^{2}$

Prism (iii),

The diagram shows a triangular prism.

The surface area of a prism can be found by adding together the area of each face.

So, surface area of the given prism $= 2 \times$ area of triangular face $+$ area of base $+$ area of side face $+$ area of sloping face

$= 2 (\frac{1}{2} \times 6 \times 8) + (6 \times 3) + (8 \times 3) + (10 \times 3)$

$= 120 {cm}^{2}$

Prism (iv),

The diagram shows a combination of two rectangular prisms.

So, surface area of the given prism $= [(6.5 \times 4) + (5.5 \times 4) + 2 (6.5 \times 1) + 2 (4 \times 1)] + [(4 \times 1) + 2 (4 \times 1) + 2 (4 \times 4)]$

$= 69 + 44 = 113 {cm}^{2}$

Thus, the completed Venn diagram for the obtained answers is given below.

Michele Conway, Belle Cottingham, Alastair Duncombe and, Amanda George Solutions for Exercise 7: Exercise 3

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