find the area and perimeter of an equilateral triangle whose height is 12 cm
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Explanation:
We know that h=12 inches.
Knowing that the triangle is equilateral makes everything easier: the heights are also medians. So the height h is perpendicular to the side AB and it divides it in two halves, which are a2 long.
Then, the triangle is divided into two congruent right triangles and the Pythagorean theorem holds for one of these two right triangles: a^2=h^2+(a^2)^2. So 3/4a^2=h^2i.e. a^2=4/3×h^2. In the end, we get that the side is given by a=8√3
Now the area:
A=a⋅h^2=8√3×(12)^2
We know that h=12 inches.
Knowing that the triangle is equilateral makes everything easier: the heights are also medians. So the height h is perpendicular to the side AB and it divides it in two halves, which are a2 long.
Then, the triangle is divided into two congruent right triangles and the Pythagorean theorem holds for one of these two right triangles: a^2=h^2+(a^2)^2. So 3/4a^2=h^2i.e. a^2=4/3×h^2. In the end, we get that the side is given by a=8√3
Now the area:
A=a⋅h^2=8√3×(12)^2
Answered by
3
Height = 12 = √3/2 * side
Side = 8√3
Perimeter = 24√3
Area = 1/2* 8√3 * 12= 48√3.
Side = 8√3
Perimeter = 24√3
Area = 1/2* 8√3 * 12= 48√3.
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