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Answer :

Ankitgo

Answer:

[tex]\fbox{ Option D ➫ \: 416 \: cm²}[/tex]

Step by step explanation:

Given:

height of prism h = 18 cm

length of base of triangle b = 10cm

height of triangle h' = 2 cm

side A of triangle = 5 cm

side B of triangle = 7 cm

To find:

Surface area of prism = ?

Solution:

[tex]Area \: of \: base \: triangle = \: \frac{1}{2}\cdot{b}{h'} \\ Area \: of \: base \: triangle = \frac{1} {\not2}\cdot{10} \times \not{2} \\ Area \: of \: base \: triangle = 10 \: {cm}^{2} [/tex]

[tex] \fbox{Area \: of \: base \: triangle \: (B) = 10 \: cm²}[/tex]

[tex]Perimeter \: of \: base \: triangle = Side A + Side B + base b \\ Perimeter \: of \: base \: triangle = 5 + 7 + 10 \: cm \\ Perimeter \: of \: base \: triangle = 22 \: cm[/tex]

[tex] \fbox{Perimeter \: of \: base \: triangle (p) \: = 22 \: cm}[/tex]

[tex]Surface \: area \: of \: prism = 2B+ \: ph \\ Surface \: area \: of \: prism = 2 \times 10+ \: 22 \times 18 \\ Surface \: area \: of \: prism = 20 + 396\\ Surface \: area \: of \: prism = 416 \: {cm}^{2} [/tex]

[tex]\fbox{Surface \: area \: of \: prism = 416 \: cm²}[/tex]

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Answer:

D. 416 cm²

Step-by-step explanation:

Let S be the surface area of the prism

     B be the area of the base of the prism

     A be the lateral area of the prism

_______

formula :

S = 2B + A

__________

The base is a triangle ,then B the area of the base :

[tex]B=\frac{10 \times 2}{2}=10 \mathrm{~cm}^{2}[/tex]

_______

formula :

A = (Perimeter of the base) × (the height of the prism)

__________

then ,

[tex]\begin{aligned}A &=(10+5+7) \times 18 \\&=22 \times 18 \\&=396cm^2\end{aligned}[/tex]

Conclusion:

[tex]\begin{aligned}S &=2 B+A \\&=2 \times(10)+396 \\&=20+396 \\&=416 \mathrm{~cm}^{2}\end{aligned}[/tex]

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