Question

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

correct 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.

Answer 1

just had this question :/ 108√3

Explanation:

Answer 2

`\boxed{108√(3)\text{ in}^(2)}`

Explanation:

An apothem is a perpendicular drawn from the centre of the triangle to one of its sides.

The three apothems OD, OE, and OF divide ∆ABC into six smaller congruent triangles.

1. Area of ∆OCD

CotOCD = OD/OC

cot30 = CD/6

√3 = CD/6

CD = 6√3

A= ½bh

A = ½ × 6√3 × 6 = 18√3 in²

2. Area of ∆ABC

A = 6 × area of ∆OCD = 6 × 18√3 = 108√3 in²

`\text{The area of the triangle is }\boxed{108 √(3) \text{ in}^(2)}`