# Square and circles

The square in the picture has a side length of a = 20 cm. Circular arcs have centers at the vertices of the square. Calculate the areas of the colored unit. Express area using side a.

### Correct answer:

#### 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: video1

## Related math problems and questions:

- Eq triangle minus arcs

In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts - Equilateral triangle v3

Calculate the content of the colored gray part. Equilateral triangle has side length 8 cm. Arc centers are the vertices of a triangle. - Circles

The areas of the two circles are in the ratio 2:20. The larger circle has a diameter 20. Calculate the radius of the smaller circle. - Inscribed circle

The circle inscribed in a triangle has a radius 3 cm. Express the area of the triangle using a, b, c. - Arc and segment

Calculate the length of circular arc l, area of the circular arc S_{1}and area of circular segment S_{2}. Radius of the circle is 11 and corresponding angle is ?. - Ratio of squares

A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares? - Arc-sector

arc length = 17 cm area of sector = 55 cm^{2}arc angle = ? the radius of the sector = ? - Common chord

Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles? - Annulus

Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus. - Rectangle diagonals

It is given a rectangle with an area of 24 cm^{2}a circumference of 20 cm. The length of one side is 2 cm larger than the length of the second side. Calculate the length of the diagonal. Length and width are yet expressed in natural numbers. - Quarter of a circle

Calculate the circumference of a quarter circle if its content is S = 314 cm^{2}. - Concentric circles and chord

In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord? - Hexagonal pyramid

Calculate the surface area of a regular hexagonal pyramid with a base inscribed in a circle with a radius of 8 cm and a height of 20 cm. - Pendulum

Calculate the pendulum's length that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm. - Water in aquarium

The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water. - 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? - Diagonals

Given a rhombus ABCD with a diagonalsl length of 8 cm and 12 cm. Calculate the side length and content of the rhombus.