Question

the side of square based prism is 2.5cm and it's height is 6.5 cm . find it's lateral and total surface area
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Answer 1

♻️ANSWER♻️

The perimeter P of the prism is P=4×side, therefore, the perimeter of prism with side 2.5 cm is P=4×2.5=10 cm.

The general formula for the lateral surface area of a right prism is LSA=Ph where P represents the perimeter of the base and h represents the height of the prism.

Since the perimeter of the prism is P=10 cm and the height is h=6.5 cm, therefore, the lateral surface area is:

LSA=P×h=10×6.5=65 cm ²

The general formula for the total surface area of a right prism is TSA=Ph+2B where P represents the perimeter of the base, h is the height of the prism and B is the area of the base.

Since LSA=Ph=65 cm ²

and the base is B=2.5 cm, therefore, the total surface area is:

TSA=2(2.5) ²+65=12.5+65=77.5 cm ²

Hence, lateral surface area is 65 cm ²

and total surface area is 77.5 cm ²

Answer 2

$\pink{\underline{\underline{Answer:}}}$

Given,

• Side of square = 2.5cm

• Height = 6.5cm

To Find:-

---->Lateral surface area

----->Total surface area.

Calculations:-

LSA = P×h

LSA = lateral surface area

p = Perimeter

h=height

Firstly we have to find the perimeter:-

Perimeter of prism =4×side

=4×2.5

=10cm

Now,

LSA =P×h

Substituting the given values:-

=10×6.5

$= {65cm}^{2}$

TSA =Ph+2B

TSA =total surface area

p=perimeter

h=height

B=base

substituting the given values:-

TSA=65+2×2.5×2.5

=65+2(2.5)^2

=65+2×10

=65+20

$= {85cm}^{2}$