Planimetrics + square - practice problems - page 15 of 65
Number of problems found: 1286
- Square room
What is the size of the smallest square room, which can be paved with tiles with dimensions of 55 cm and 45 cm? How many such tiles are needed? - Rectangle - sides 3
If in the rectangle ABCD, we enlarge side a by 5 cm and decrease side b by 2 cm, the rectangle area will be reduced by 5 cm². When we decrease the length of side a by 4 cm, and at the same time we increase the length of side b by 3 cm, we increase the are - Rectangles - sides
One side of the rectangle is 10 cm longer than a second. Shortening the longer side by 6 cm and extending the shorter by 14 cm increases the rectangle area by 130 cm². What are the dimensions of the original rectangle? - Constructed 8161
The perimeter of the right triangle is 18 cm. The sum of the areas of the squares constructed above its three sides is 128cm². What is the area of the triangle?
- Difference 3994
In a trapezoid, the difference is a base of 6 cm. Calculate the lengths of the bottom of a trapezoid when its height is 8 cm and the area of the trapezoid is 168 cm square. - Dimensions 3159
The rectangle is 6 cm longer than the width. A square with a side equal to the length of the rectangle has an area of 78 cm² larger than the rectangle. Calculate the dimensions of the rectangle. - Circle and square
An ABCD square with a side length of 100 mm is given. Calculate the circle’s radius that passes through vertices B, C, and the center of the side AD. - Diamond diagonals
Find the diamond diagonal's lengths if the area is 156 cm² and the side is 13 cm long. - Diamond diagonals
Calculate the diamonds' diagonal lengths if the diamond area is 156 cm square and the side length is 13 cm.
- Trapezoid
How long are the trapezoid bases with an area of 24 cm² and a height of 3 cm? One base is three times longer than the shorter. - Approximate 83298
They planted 5,600 tulips in the garden bed, an average of 50 tulips per 1 m². What is the approximate size of the flower bed? - Perimeter 31761
Mr. Marek wants to build a circular pond in his garden. He wishes the perimeter of the pond in meters and the area in square meters to be expressed in the same numbers. What is the radius of the pond? - Six-fourteenths 7295
Seven twelfth windows in the castle are in the shape of an n-gon. Six-fourteenths of these windows are quadrangular in shape, while two-ninths of them are square windows. How many windows are there in the castle if there are 15 square windows? - Isosceles 5711
An isosceles triangle with a base length of 32 cm has an area of 480 cm². What's his perimeter?
- Outside point
The square ABCD and the point E lying outside the given square are given. What is the area of the square when the distance | AE | = 2, | DE | = 5 a | BE | = 4? - Two circles
Two circles with the same radius, r = 1, are given. The center of the second circle lies on the circumference of the first. What is the area of a square inscribed in the intersection of given circles? - Land
Rectangular, triangular land has an area of 30 square meters and 12 meters long leg. How many meters of fence do you need for fencing this land? - Diamond diagonals
Calculate the diamond's diagonal lengths if its area is 156 cm² and the side length is 13 cm. - A goat
In the square garden of side (a), a goat is tied in the middle of one side. Calculate the length of the rope (r) so that the goat grazes exactly half the garden. If r = c * a, find the constant c.
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