Question

is the ans i got correct?
the total surface area is 33.8cm²
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Answer 1

Given:

A prism with height 5 cm and equilateral triangular base with side 2 cm.

To find:

The total surface area of the prism.

Solution:

Area of an equilateral triangle is:

$A_1=\dfrac{\sqrt{3}}{4}a^2$

Where, a is the side length.

Putting $a=2$, we get

$A_1=\dfrac{\sqrt{3}}{4}(2)^2$

$A_1=\dfrac{\sqrt{3}}{4}(4)$

$A_1=\sqrt{3}$

$A_1\approx \sqrt{3}$

The base and top of the prism are congruent so their area must be equal.

The lateral surface area of the prism is:

$LA=Ph$

Where, P is the perimeter of the base and h is the height of the prism.

The lateral surface area of the prism is:

$A_2=(2+2+2)5$

$A_2=(6)5$

$A_2=30$

Now, the total surface area is the sum of areas of bases and lateral surface area.

$A=2A_1+A_2$

$A=2(1.73)+30$

$A=3.46+30$

$A=33.46$

Therefore, the total surface area is 33.46 cm².