Quadratic equation + area of a shape - practice problems - last page
Number of problems found: 119
- Square grid
A square grid consists of a square with sides of a length of 1 cm. Draw at least three patterns, each with an area of 6 cm² and a circumference of 12 cm, and their sides in a square grid. - Rectangle
The perimeter of the rectangle is 22 cm, and the area is 30 cm². Determine its dimensions if integers express the length of the sides of the rectangle in centimeters. - The hall
The hall had a rectangular ground plan, one dimension 20 m longer than the other. After rebuilding, the length of the hall declined by 5 m, and the width increased by 10 m. The floor area increased by 300 m². What were the original dimensions of the hall? - Circular flowerbed
We split the circular flowerbed with diameter 8 m by concentric circle to circle and annulus with the same area. Find the radius of the circle.
- Orchard
The route passes the trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3. The length of the longer base to the size of the path is in the ratio of 5:6. How many square meters occupy the - Perimeter and legs
Determine the perimeter of a right triangle if the length of one leg is 75% length of the second leg, and its area is 24 cm². - Triangle
Calculate the triangle sides if its area S = 630 and the second cathetus is shorter by 17. - Do you solve this?
Determine area S of a rectangle and the length of its sides if its perimeter is 102 cm. - Diagonals in the diamond
The length of one diagonal in a diamond is 24 cm greater than the length of the second diagonal, and the diamond area is 50 m². Determine the sizes of the diagonals.
- Tiles
From how many tiles, 20 cm by 30 cm, we can build a square of maximum dimensions if we have maximum 275 tiles. - Rectangle - sides
A rectangle has an area 266 cm². The length of the shorter side is 5 cm fewer than the length of the longer side. What is the perimeter of a rectangle? - Rhombus
The rhombus with area 137 has one diagonal that is longer by 5 than the second one. Calculate the length of the diagonals and rhombus sides. - Garden
The square garden area is 2/9 of triangle garden with sides 160 m, 100 m, and 100 m. How many meters of fencing need to fence a square garden? - Coins
Edmund had saved a certain number of 2-euro coins. He placed the coins in a single layer in a square. He has 6 coins left. When he wanted to build a square that would have one more row, he was missing 35 coins. How many euros does he have?
- Trapezoid MO
The rectangular trapezoid ABCD with the right angle at point B, |AC| = 12, |CD| = 8, diagonals are perpendicular to each other. Calculate the perimeter and area of the trapezoid. - Resistors
Two parallel resistors connected in series give the resulting resistance $R1Ω and $R2Ω. Determine the resistance of these resistors. - Heron backlaw
Calculate the missing side in a triangle with sides 25 and 13 and area 152. - Rectangle
The area of a rectangle is 546. Its length is 25 larger than the width. What are the dimensions of the rectangle? - Right triangle Alef
The obvod of a right triangle is 84 cm, and the hypotenuse is 37 cm long. Determine the lengths of the legs.
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