# Area - high school - examples

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. Axial section
Axial section of the cone is an equilateral triangle with area 208 dm2. Calculate the volume of the cone.
3. Square
Points A[-5,-6] and B[7,-1] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.
4. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
5. Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
6. Right triangle Alef
The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
7. Pipes
Water pipe has a cross-section 1087 cm2. An hour has passed 960 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 9 hours if water flow same speed?
8. 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.
9. Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
10. Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
11. Gutter
How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material.
12. Pentagon
Calculate the area of regular pentagon, which diagonal is u=17.
13. Sandpile
Auto sprinkled with sand to an approximately conical shape. Workers wanted to determine the volume (amount of sand) and therefore measure the circumference of the base and the length of both sides of the cone (over the top). What is the volume of the san
14. R triangle
Calculate the area of a right triangle whose longer leg is 6 dm shorter than the hypotenuse and 3 dm longer than the shorter leg.
15. Pyramid roof
1/3 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 9 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
16. Tetrahedral pyramid
Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
17. Sphere slices
Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
18. Area of RT
In the right triangle has orthogonal projections of legs to the hypotenuse lengths 7 cm and 12 cm. Determine the area of ​​this triangle.
19. Pillar
Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
20. Built-up area
John build up area 5 x 7 = 35 m2 with building with a wall thickness 30 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 9%?

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