Question

What is the area, rounded to the nearest tenth of square inch, of an equilateral triangle that has a perimeter of 24 inches?

Area = square inches

Answer 1

27.7 square inches

Explanation:

Equilateral triangle has all equal sides...so hence..each side = 8 inches

Area of a non right angled triangle

= 1/2 × ab × sin theta....where a and b are sides of the triangle...in which in this case a and b are both equal to 8....,then theta is the angle made by the two sides a and b....in which in this case its 60 degrees.

..its 60 degrees because the angles in an equilateral triangle are equal...so hence its 180÷3 = 60 degrees

then apply the formula...

Area = 1/2 × 64 × sin 60

;Area = 27.7 square inches

Answer 2

For this case we have that by definition, an equilateral triangle has its three equal sides. If the perimeter is 24 then each side measures:

`\frac {24} {3} = 8\ in`

By definition, the area of an equilateral traingulo depending on the side is given by:

`A = \frac {a ^ 2 \sqrt {3}} {4}`

Where:

a: It is the side of the triangle. In this case
`a = 8`

So:

`A = \frac {8 ^ 2 \sqrt {3}} {4}\\A = \frac {64 \sqrt {3}} {4}\\A = 16 \sqrt {3}\\A = 27.7128`

Rounding:

`A = 27.7 \ in ^ 2`

ANswer:

`A = 27.7 \ in ^ 2`