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Dimas [21]
3 years ago
9

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the corre

ct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.
Find the area of an equilateral triangle (regular 3-gon) with the given measurement.

6-inch apothem

A = sq. in

Mathematics
2 answers:
Vedmedyk [2.9K]3 years ago
7 0
A=√3/4 a²

a is the apothem and A is area:

A=√3/4(6)²

A= 9√3
grigory [225]3 years ago
7 0

Answer: 12√3 square inches

Step-by-step explanation:

By the property of equilateral triangle,

Apothem = √3/2 × Side

⇒ Side = 2/√3 × Apothem

Here, apothem = 6 inches

Thus, the side of the given equilateral triangle =  \frac{2}{\sqrt{3}}\times 6

= \frac{12}{\sqrt{3}}

= 4\sqrt{3}  unit

Since, For an equilateral triangle,

\text{ Area} = \frac{\sqrt{3}}{4}\times (\text{ side})^2

⇒ The area of the given equilateral triangle = \frac{\sqrt{3}}{4}\times (4\sqrt{3})^2

=\frac{\sqrt{3}}{4}\times 48

=12\sqrt{3}  square inches

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