What is the length of the radius of a circle inscribed in a triangle whose sides are 10, 8 and 14?

There is probably a formula for this or other ways of doing this, but I will give it a shot.

An octagon has 8 sides (octopus has 8 legs). To make an octagon, we effectively have 8 triangles joined at the centre. In the centre, we have 8 equal angles. Since a full circle is 360 degrees, each of these angles must be 360 / 8 or 45 degrees.

Now we can just focus on one of these triangles. We have an angle of 45 degrees at the centre and two arms extending out 10 feet.

At this point, we can use the cosine law to calculate the length of the side or we can recognize that it is an isosceles triangle and work out the other angles and determine the length of the side.

Using Cosine Law, a^2= b^2 + c^2 - 2xbxc Cos A
In this case, A = 45 degrees, b = 10 feet, c=10 feet.

Good luck.

Let me know if you have any questions.

Paul

What game does this relate to ?

A square is inscribed in a circle and a second circle is inscribed in the square. What is the relationship between the areas of the two circles.
Literally, squaring the circle means devising the straightedge-and-compass construction of a square whose area equals that of a given circle. T square the circle

A. The equation of a circle is (x-a)^2 + (y-b)^2 = r^2, with (a,b) being the centre of the circle and r being the radius.

Good luck,

Paul

I will not try to guess what that diameter represents, so I will give you all mensuration formulas for the area of a regular polygon.
s is the measure of the side, r the radius of the inscribed circle, R the radius of the circumscribed circle, and n the number of sides.
If the angle unit in your calculator is the degree, use 180 instead of Pi. Use the formulas with PI if angle unit is set to radians.
In the formulas on the last line of the display screen (the formulas with sine functions) the radius r should be R (circumscribed circle radius). cot is the reciprocal of the tangent function (cot(x)=1/tan(x) )

Well it depends. If the hexagon is irregular (sides are not equal) there is no formula to calculate the sides as they can have arbitrary values. You must measure them.
If the hexagon is regular you may be able to relate the measure of a side to the radius of the circle in which it is inscribed. If you have the radius of the circle, the side is equal to the radius. If you have the value of perimeter you divide that value by 6.
There is also a formula that relates the area of the hexagon to the measure of the side s. The formula is Area=(6/4)(s^2)cot(PI/6), where cot is the cotangent function, its angle is in radian. In degrees Pi/6 is 30 degrees.

Area - The size of a surface

Specific

Square
Area = Side x Side

Rectangle
Area = Length x Width

Triangle
Area = Base x Height (cut the answer in half and that is your area)

Parallelogram
Area = Base x Height

Circle
Area = Radius x Radius x 3.14

A regular hexagon is made up of six equilateral triangles. This means that the length of any one side of the hexagon is equal to the radius.

The diameter of the circle is the diagonal of the rectangle use Pythagoras this rectangle is a made from two 3,4,5 triangles, so the diameter is 5cm, the radius will be 2.5cm don't forget the BODMAS ordering rule (Brackets of Division Multiplication Addition and Subtraction) Also rounding to 2 decimal places. This solution is based on all four corners of the rectangle touching the circumference of the circle.

Area of a circle is P (22/7) i x Radius (squared ^2) ====> 22/7 x 2.5cm ^ 2 ====> 22/7 x 6.25cm

TOTAL AREA of CIRCLE = 19.64 cm^2

Area of the rectangle is length x width ====> 4 cm x 3 cm

TOTAL AREA of RECTANGLE = 12 cm ^2

The remaining portion is the circle area minus the rectangle 19.64-12 = 7.64 cm^2


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how big is the triangle? if the coins are a mile in diameter doesnt mean you cant have an equilateral triangle with legs of 32 miles long.

or are you asking for the equation?

i will send you on the path to the equation.

if you draw a circle on a piece of paper then draw a triangle around it where is the center? if the triangle were a perfect equilateral then the circle would be a perfect circle touching the sides of the triangle.

its important to know where the center is because the center of the circle to the edge of the circle is the radius.

so the center of a triangle is the center of the circle. therfeore the radius of the circle will equal hieght/2...

thinking that way you can say that if there were three coins then the center of the triangle cant be occupied by a coin but is very close to an edge. where is the center of the coin?

If an arc is 4╥, it is 12.56.
You can use 12.56 as a starting point and figure out what circumference that is 40° of.

Circumference = 2 • π • radius = π • diameter

Reverse this and you will have your answer.