Silver medal

To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?

Correct result:

S =  50 cm2

Solution:

$D=10 \ \text{cm} \ \\ D^2=a^2 + (3a)^2 \ \\ D^2=a^2 + 9a^2 \ \\ D^2=10 \ a^2 \ \\ \ \\ D=\sqrt{ 10 } a \ \\ a=D / \sqrt{ 10 }=10 / \sqrt{ 10 } \doteq \sqrt{ 10 } \ \text{cm} \doteq 3.1623 \ \text{cm} \ \\ n=5 \ \\ \ \\ S=n \cdot \ a^2=5 \cdot \ 3.1623^2=50 \ \text{cm}^2$

Our examples were largely sent or created by pupils and students themselves. Therefore, we would be pleased if you could send us any errors you found, spelling mistakes, or rephasing the example. Thank you!

Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

Be the first to comment!

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

You need to know the following knowledge to solve this word math problem:

We encourage you to watch this tutorial video on this math problem:

Next similar math problems:

• Circular lawn
Around a circular lawn area is 2 m wide sidewalk. The outer edge of the sidewalk is curb whose width is 2 m. Curbstone and the inner side of the sidewalk together form a concentric circles. Calculate the area of the circular lawn and the result round to
• Logs
The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
• Round table
Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes?
• Tangent 3
In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
• Quatrefoil
Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
• Regular octagon
Draw the regular octagon ABCDEFGH inscribed with the circle k (S; r = 2.5 cm). Select point S' so that |SS'| = 4.5 cm. Draw S (S '): ABCDEFGH - A'B'C'D'E'F'G'H'.
• Cutting circles
From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste?
• Squaring the Circle
Calculating side of the square with the same area as the circle of radius 18.
• Percentage of waste
In a square plate with side 75 cm we cut 4 same circles. Calculate the percentage of waste.
• Concentric circles
There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
• Ace
The length of segment AB is 24 cm and the point M and N divided it into thirds. Calculate the circumference and area of this shape.
• Inscribed circle
The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c.
• Holidays - on pool
Children's tickets to the swimming pool stands x € for an adult is € 2 more expensive. There was m children in the swimming pool and adults three times less. How many euros make treasurer for pool entry?
• Surveyor
Calculate the area of ​​what may vary rectangular, if it focused by surveyor and found the dimensions 18 x 15 m while in each of the four joint points can be position deviation 25 cm?
• The right triangle
The right triangle ABC has a leg a = 36 cm and an area S = 540 cm2. Calculate the length of the leg b and the median t2 to side b.
• Perimeter of the circle
Calculate the perimeter of the circle in dm, whose radius equals the side of the square containing 0.49 dm2?
• Circle's chords
In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.