# Area of shape - 9th grade (14y) - examples

1. Perimeter of RT
Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
2. 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?
3. Percent change
If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.
5. Pyramid height
Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
6. 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.
7. Garden
Area of a 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?
8. Right Δ
A right triangle has the length of one leg 28 cm and length of the hypotenuse 53 cm. Calculate the height of the triangle.
9. Tetrahedral pyramid
What is the surface of a regular tetrahedral (four-sided) pyramid if the base edge a=7 and height v=6?
10. Triangle SAS
Calculate the area and perimeter of the triangle, if the two sides are 51 cm and 110 cm long and angle them clamped is 130 °.
11. Square
Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
12. Rhombus
Calculate the perimeter and area of ​​a rhombus whose diagonals are 38 cm and 55 cm long.
13. Scale
Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
14. Regular 5-gon
Calculate area of the regular pentagon with side 7 cm.
15. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
16. Rectangle
In rectangle with sides, 10 and 8 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
17. Area of RT
Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5.
18. Circles
The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
19. Cylinders
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
20. Widescreen monitor
Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of ​​the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha

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