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What is the area of an equilateral triangle of side length 20 cm?

Answer 1

Mason Adams

#100sqrt(3)#

Referring to this image, https://tutor.hix.ai(11)png we know that #AB=AC=BC=20#.

This means that the height cuts #AB# in two equals parts, #AH# and #HB#, each #10# units long.

This means that, for example, #AHC# is a right triangle with #AC=20# and #AH=10#, so

#CH = sqrt(AC^2-AH^2) = sqrt(20^2-10^2)=sqrt(300)=10sqrt(3)#

Since we know the base and the height, then the area is

#(20*10sqrt(3))/2 = 100sqrt(3)#

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Answer 2

Parker Allen

The area ( A ) of an equilateral triangle with side length ( s ) can be calculated using the formula:

[ A = \frac{\sqrt{3}}{4} \times s^2 ]

Given that the side length ( s ) is 20 cm, we can substitute this value into the formula to find the area of the equilateral triangle:

[ A = \frac{\sqrt{3}}{4} \times (20)^2 ]

[ A = \frac{\sqrt{3}}{4} \times 400 ]

[ A = \frac{\sqrt{3} \times 400}{4} ]

[ A = \frac{400\sqrt{3}}{4} ]

[ A = 100\sqrt{3} ]

Therefore, the area of the equilateral triangle with side length 20 cm is ( 100\sqrt{3} ) square centimeters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.