I am going to assume you mean the by radius of the equilateral triangle, you mean the radius of the circumcircle of the triangle. This is the circle that passes through all 3 vertices of the triangle. This is 8
The apothem is 4 and it is the short vertical line from the center to the midpoint of an edge.
Construct a right triangle with the one side being the apothem and the hypotenuse being the radius. The length of the other side ( the missing one for which you are solving) is 1/2 the length of the side of the equilateral triangle. A picture will help you see this.
Now area will be this times the altitude of the triangle.
Or you can directly use the fact the the area is (square root of 3 )/ 4 x (the length of the side squared. )
So in this case 1/2 the length of the side is square root of 48 or 4(square root 3)
Now to find the area we square this entire quantity after we multiply it be 2 since it was half the side and multiply by (Square root of 3)/ 4.
So the side length is 2(sqrt 48) or 8(sqrt 3)
When you square this you have 192 now to finish just multiply this by (sqrt3)/4 to find area. I come up with 48(sqrt(3)) mm2
You can also use the fact that radius=side length x (sqrt3)/4 and solve for side length.
This gives you side length = 3(radius) divided by square root of 3.
Once again, you have side length is 8(sqrt 3)
One last method. Once you found side length is 8(sqrt 3) you know that height or altitude of the triangle is 12. Now use 1/2 base x height and you have the exact same answer.
Or,
The apothem of an equilateral triangle is 1/3 of the median, which is also the height of the triangle. So the height is 12 mm (4 x 3). In one of the right triangles that are formed by drawing the height, we have:
one half of the base = cot 60 degrees x height
base = 2(cot 60 degrees x height)
So that the area of the triangle is:
A = (base x height)/2
A = [2(cot 60 degrees x height)(height)]/2
A = cot 60 degrees x height2
A = cot 60 degrees x (12 mm)2
A = 83.14 mm2 (approximately)
Area = 8.06 cm2.
the perimeter is 36 and the area is 144
For a SQUARE, the area is (2r)2 because the length and width are the same. The apothem (radius) is used to find the area of other regular polygons.
Area = 0.5*base*altitude
297 M
Area = 8.06 cm2.
the perimeter is 36 and the area is 144
The area is 9.2376 units squared.
The area is 9.2376 square feet.
The area is 11.69 square units.
Area of Equilateral Triangle A= S2 * (Root 3)/4, where A= Area of the triangle S= Side of the triangle.
5.7735 cm is the length of a side so 1/2 x base x Height should give you an answer. Remember, the apothem makes two mirrored 30 60 right triangles...Pythagoras will tell you how to find the hypotenuse...that will be the unknown side of the equilateral.
For a SQUARE, the area is (2r)2 because the length and width are the same. The apothem (radius) is used to find the area of other regular polygons.
A regular pentagon has five (5) equilateral triangles within it. Find the area of each triangle (1/2bh where b is the base of the triangle or the length of a side of the pentagon, and h is the height of the triangle or the apothem of the pentagon) and multiply the area of the triangle times five (5).
If an equilateral triangle and a square have equal perimeters, then the ratio of the area of the triangle to the area of the square is 1:3.
Perimeter of equilateral triangle: 24 units Area of equilateral triangle: 27.713 square units rounded to three decimal places
A triangle has area, not volume.