# Examples of area of plane shapes

1. Isosceles triangle 9
Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle
2. Ratio of volumes
If the heights of two cylindrical drums are in the ratio 7:8 and their base radii are in the ratio 4:3. What is the ratio of their volumes?
3. Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
4. Ratio of sides
Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
5. A rectangular patio
A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
6. A photograph
A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo.
7. Rectangular garden 2
A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
8. 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.
9. Iceberg
What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
10. 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?
11. 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?
12. Triangular prism
Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
13. Masquerade ball
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.
14. Pyramid height
Find the volume of a regular triangular pyramid with edge length a = 12cm and pyramid height h = 20cm.
15. Decorative fence
The rectangular garden is 57 m long and 42 m wide. Calculate how much m² it will reduce if it encloses with a 60 cm wide decorative fence.
16. The sides 2
The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
17. Area of rectangle
How many times will increase the area of the rectangle, if we increase twice the length and at the same time we decrease the width by the half?
18. A screen
A screen is 1680 x 1050 pixels. What are the coordinates (and size in pixels) of an centered area which is exactly 33% of the screen size?
19. In the
In the national park, the ratio of the wooded area to grassland is 4: 1. The total area is 385km2. What area is wooded?
20. Rectangle
There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle.

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