What is the ratio of the area of an equilateral triangle to the area of its Circumcircle?

We know that area of circle = π*r2, where r is the radius of given circle. We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3. Therefore, area = π*r2 = π*a2/3.

What is the ratio of the area of circle inscribed in an equilateral triangle?

Area of a equilateral triangle is sqrt3/4 a^2. Area of circle is pi r^2. r = 2/3 × sqrt3/2 ×a = a/sqrt3.

What is the ratio of equilateral triangle?

The height of an equilateral triangle divides it into two equal 30:60:90 triangles, which will have side ratios of 1:2:√3.

What is the ratio of the areas of circles inscribed and circumscribed in a square?

Let the side of the square inscribed in a square be a units. Hence, the required ratio is 2 : 1.

What is the ratio of the areas of the incircle and circumcircle of a square?

Required ratio = πx24 : πx22 = 14 : 12 = 1 : 2.

What is the ratio between area of square inscribed in a circle and equilateral triangle circumscribed about the same circle?

radius of circumcircle : radius of incircle = 2:1. Therefore, for any equilateral triangle, area of circumcircle : area of incircle = 4:1.

What is the ratio of the diameter of the circles inscribed in and circumscribing an equilateral triangle to its height?

∴ Required ratio = a√3 : 2a√3 2 a 3 : √32a 3 2 a = 2a : 4a : 3a = 2 : 4 : 3.

What is the formula of area of equilateral?

In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3s/ 2 * s = √3s2/4.

What is the ratio of a right triangle?

45°–45°–90° triangle The sides in this triangle are in the ratio 1 : 1 : √2, which follows immediately from the Pythagorean theorem. Of all right triangles, the 45°–45°–90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, namely √22.

What is the base to height ratio of an equilateral triangle?

Question: The ratio of base to height of an equilateral triangle is 3:4 .

How do you find the square of maximum area of a triangle?

The square of maximum area occurs when upper corners of square touches the sides of the equilateral triangle and the bottom side of the square is on one side of the triangle.

What is the relation between the area of Square and equilateral triangle?

The square of maximum area occurs when upper corners of square touches the sides of the equilateral triangle and the bottom side of the square is on one side of the triangle. Then you can find the relation between the area of square and the equilateral triangle.

What happens when a circle is inscribed in an equilateral triangle?

A circle is inscribed in an equilateral triangle and a square is inscribed in the circle. The ratio of the area of the triangle to the area of the square is Clearly, centre of triangle , circle and square coincides.

How do you find the largest equilateral triangle inside a triangle?

Based on my answer to the question Finding the largest equilateral triangle inside a given triangle, I present the following solution: Draw the diagonal BD, and draw circles with radius BD at both ends. Mark E, the intersection of the two circles, and draw intervals EB and ED.