# Recursion squares

In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm.

Calculate:
a) the sum of perimeters of all squares
b) the sum of area of all squares

Result

Σ p =  300.45 cm
Σ S =  968 cm2

#### Solution:

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

Be the first to comment!

## Next similar examples:

1. Parallelogram
Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
2. Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm?
3. Garden
Area of square garden is 6/4 of triangle garden with sides 56 m, 35 m and 35 m. How many meters of fencing need to fence a square garden?
4. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
5. Triangle SAS
Calculate area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130°.
6. Rhombus
Calculate the perimeter and area of ​​rhombus whose diagonals are 38 cm and 55 cm long.
7. Trapezoid MO-5-Z8
ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A
8. Trapezoid MO
The rectangular trapezoid ABCD with right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of ​​the trapezoid.
9. Circular pool
The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
10. Circle section
Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
11. 30-gon
At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
12. Rhombus
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.