Question

I have already done Number one but I need help with 2. Please help when you find time to!

Answer 1

❍ Concept :-

We can solve these questions by using the formulas of area of triangle and rectangle, which will make our work easier. So, we know that,

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`\blue{ \underline{ \boxed{ \begin{array}{cc} \sf1. ~Area_(Triangle) = \frac{1} {2} * b * h \qquad \: \: \: \: \: \: \: \\ \\ \\ \sf2. \: Area_(Rectangle) = Length * Breadth \end{array}}}} \\ \\`

Using these formulas and figuring out the number of triangles and rectangles in each shape, we will solve this question.

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✰ Solution :-

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1. In this square pyramid, if we closely observe, we will get to know that there are 1 rectangle and 4 triangular faces. Thus,

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`\sf \hookrightarrow Area=6 * 6 + 4( (1)/(2) * 6 * 14) \\ \\ \\ \sf \hookrightarrow Area=36 + 168 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {204 \: yd}^(2) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\`

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2. Now, here, we can use the formula of total surface area for cuboid, i.e.

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TSA = 2( lb + bh + hl )

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`\sf \hookrightarrow Area=2(10 * 6 + 6 * 3 + 10 * 3) \\ \\ \\ \sf \hookrightarrow Area=2(60 + 18 + 30) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=2 * 108 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {216 \: mm}^(2) \: \: \qquad \qquad \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\`

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Extra Credit Question.

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Here, we can find out the total surface area by finding,

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Base area i.e. length x breadth ( B.A. )

Side area i.e. length x breadth ( S.A. )

triangular area = 1/2 x b x h ( T.A. )

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Now,

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TSA = BA + 2 x S.A. + 2 x T.A.

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`\sf \hookrightarrow Area=(10 * 3) + 2(10 * 2.5) + 2((1)/(2) * 3 * 2) \\ \\ \\ \sf \hookrightarrow Area= 30 + 2 * 25 + 2 * 3 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area=30 + 50 + 6 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \sf \hookrightarrow Area= {86 \: mm}^(2) \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\`

Answer 2

Explanation:

Formulae

Area of a triangle = 1/2 x base x height

Area of a rectangle = width x length

Question 1

Surface area of square based pyramid = area of base + 4 × area of triangle

⇒ SA = (6 × 6) + 4(1/2 × 6 × 14)

= 36 + 168

= 204 yd²

Question 2

Surface area of a cuboid = 2 × base area + 2 × end area + 2 × side area

⇒ SA = 2(10 × 6) + 2(6 × 3) + 2(10 × 3)

= 120 + 36 + 60

= 216 mm²

Extra credit question

Surface area of a triangular based prism = base area + 2 × triangle area + 2 × side areas

base area = 3 × 10 = 30 mm²

triangle area = 1/2 × 3 × 2 = 3 mm²

side area = 10 × 2.5 = 25 mm²

⇒ total SA = 30 + (2 × 3) + (2 × 25)

= 30 + 6 + 50

= 86 mm²