Maths practice for 12-year-olds - page 357 of 359

Number of problems found: 7168

Trapezium zoom
By how many times does the area of a trapezoid increase if all its sides and height are multiplied by 5?
Sumo competition
In a heaviest-man competition there were 5 competitors. The top three together weighed 369 kg. What is the minimum possible weight of the winner, given that contestants' weights are measured to the nearest kilogram?
Triangle angles
The angles α, β, and γ of triangle ABC are in the ratio 6:2:6. Calculate the size of each angle.
Degrees to radians
Convert magnitude of the angle α = 538°38'17" to radians:
Rectangle A2dim
Calculate the missing side of a rectangle whose area is 950 m² and one side is 38 m long.
Window
Peter knocked a 100 × 67 cm opening in the wall for a window frame. When the glazier installs the frame and glass, the glass will be 13.5 cm from the edge of the opening on each side. By what percentage less light enters through the glass than through the
VAT
VAT is a tax on which the state artificially betrays goods and services for final consumption. VAT in Slovakia is 20%. Calculate how much percent pay fewer tax residents of Japonska when VAT is only 5%.
Solidarity
Calculate how many kilograms of salt a citizen effectively 'donates' to the government through taxes each year, if the combined tax burden (VAT + income tax + other levies) is 53% of a gross monthly salary of 982 euros and 1 kg of salt costs 15 cents.
Density - simple example
Material of density of 1189 kg/m³ occupies a container volume of 64 cm³. What is its mass?
Circle arc
A circular sector has an arc length of 9.08 km and an area of 58.99 km². Calculate the radius of the circle and the size of the central angle.
Insurance
The house owner is insured against natural disasters and pays 0.05% annually of the value of the house 88 Eur. Calculate the value of the house. Calculate the probability of disaster if you know that 50% of the insurance is to pay damages.
Garden
A trapezoid-shaped garden has parallel sides of 19 m and 24 m. Its area is 193.5 square metres. What is the height of the trapezoid?
Rectangular trapezoid
How many interior right angles does a right-angled trapezoid have?
Present
A gift box has the shape of a cuboid with dimensions 8 × 8 × 3 cm. Miloslav wants to wrap it using square sheets of paper with sides of 18 cm. How much paper is left over?
Monkey
The monkey fell into 20 meters deep well. Every day it climbs 3 meters, at night it drops back by 2 m. On what day it gets out from the well?
Mine
The wheel in a mine hoist has a diameter of 4 m. How many metres does the elevator cabin travel if the wheel rotates 89 times in the same direction?
Clocks
How far does the tip of a clock's minute hand travel in 340 minutes if the minute hand is 23 cm long? How far does the tip of the hour hand travel in the same time?
Kites
Boys fly kites on cables 68 metres long. What is the altitude of a kite if the cable makes an angle of 72° with the horizontal?
Shape
A plane figure has a maximum area of 677 mm². Calculate its perimeter if the perimeter is to be as small as possible.
Maximum area of rhombus
At what interior angles does a rhombus have the maximum area?

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