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Yuliya22 [10]
2 years ago
13

Use the net as an aid to compute the surface area (rounded to the nearest integer) of the triangular pyramid with an equilateral

triangle base.
A) 224 m2
B) 240 m2
C) 254 m2
D) 270 m2

Mathematics
1 answer:
aleksandrvk [35]2 years ago
3 0

Answer:

Correct answer is C)\ 254\ m^{2}

Step-by-step explanation:

As per the given diagram, we know the following details:

Height of the triangular pyramid is <em>14m</em>.

<em>Side of base</em> = <em>10m </em>

Height of Triangular base = <em>8.7m</em>

Formula for <em>surface area of triangular pyramid</em>:

\text{Area = Area of Triangular base + 3 }\times\text{Area of side triangle}

(Triangular base is shown in the dotted lines in the question figure.

The other 3 triangles are the side triangles.)

We know that,

\text{Area of a triangle = }\dfrac{1}{2} \times \text{Base} \times \text{Height}

\Rightarrow \text{Required Surface Area = } \dfrac{1}{2} \times 8.7 \times 10 + 3 \times \dfrac{1}{2} \times 14 \times 10\\\Rightarrow \dfrac{1}{2}\times (87 + 3 \times 140)\\\Rightarrow \dfrac{1}{2}\times (87 + 420)\\\Rightarrow \dfrac{1}{2} \times 507\\$\approx$ 254 m^{2}

Hence correct answer is C)\ 254\ m^{2}.

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