Area - 9th grade (14y) - examples
- Hypotenuse - RT
A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
- The room
The room has a cuboid shape with dimensions: length 50m and width 60dm and height 300cm. Calculate how much this room will cost paint (floor is not painted) if the window and door area is 15% of the total area and 1m2 cost 15 euro.
- Coordinate axes
Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y.
Area of square garden is 4/5 of triangle garden with sides 24 m, 15 m and 15 m. How many meters of fencing need to fence a square garden?
- Right Δ
Right triangle has length of one leg 51 cm and length of the hypotenuse 85 cm. Calculate the height of the triangle.
- Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
Points A[-9,6] and B[-5,-3] are adjacent vertices of the square ABCD. Calculate area of the square ABCD.
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?
- Cone A2V
Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone.
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 254 cm2.
- Right triangle Alef
The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
The areas of the two circles are in the ratio 2:14. The larger circle has diameter 14. Calculate the radius of the smaller circle.
Water pipe has a cross-section 1405 cm2. An hour has passed 756 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 15 hours if water flow same speed?
- 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
- Circle arc
Circle segment has a circumference of 41.89 m and 251.33 m2 area. Calculate the radius of the circle and size of central angle.
- Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
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.
Calculate the area of regular pentagon, which diagonal is u=19.
- 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.
- Sand pile
Auto sprinkled with sand to 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 sand c
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