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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

Respuesta :

thedemon840

Answer:

27.7 square inches

Step-by-step 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

carlosego

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:

[tex]\frac {24} {3} = 8\ in[/tex]

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

[tex]A = \frac {a ^ 2 \sqrt {3}} {4}[/tex]

Where:

a: It is the side of the triangle. In this case[tex]a = 8[/tex]

So:

[tex]A = \frac {8 ^ 2 \sqrt {3}} {4}\\A = \frac {64 \sqrt {3}} {4}\\A = 16 \sqrt {3}\\A = 27.7128[/tex]

Rounding:

[tex]A = 27.7 \ in ^ 2[/tex]

ANswer:

[tex]A = 27.7 \ in ^ 2[/tex]

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