# Area + system of equations - practice problems

#### Number of problems found: 64

- Two gardens

The total area of the two gardens is 864 m². The first garden is 60 m² smaller than three times the second garden. What is the area of each garden? - Three faces of a cuboid

The diagonal of three faces of a cuboid are 13,√281, and 20 units. Then the total surface area of the cuboid is. - Two patches

Peter taped the wound with two rectangular patches (one over the other to form the letter X). The area sealed with both patches at the same time had a content of 40cm² and a circumference of 30cm. One of the patches was 8cm wide. What was the width of the - Rectangular garden

The perimeter of Peter's rectangular garden is 98 meters. The width of the garden is 60% shorter than its length. Find the dimensions of the rectangular garden in meters. Find the garden area in square meters. - Rectangle field

The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m? - Flowerbed

We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius. - Two cubes

The surfaces of two cubes, one of which has an edge of 22 cm longer than the second are differ by 19272 cm². Calculate the edge length of both cubes. - Parallelogram

The sides of the parallelogram are 8 cm and 6 cm long, and the diagonals' angle is 60°. What is its area? - Rectangular plot

The dimensions of a rectangular plot are (x+1)m and (2x-y)m. If the sum of x and y is 3m and the perimeter of the plot is 36m. Find the area of the diagonal of the plot. - Rectangular triangle

The lengths of the rectangular triangle sides with a longer leg of 12 cm form an arithmetic sequence. What is the area of the triangle? - Tractors

Wheel and belt tractors each day plow 8 ha of fields. For plow 76 hectares, the wheel would have to work for 12 days and 8 days with the belt tractor together. How many hectares do each day of each tractor? - AP RT triangle

The length of the sides of a right triangle forms an arithmetic progression, and the longer leg is 24 cm long. What are the perimeter and area? - Right triangle eq2

Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70. - Solid cuboid

A solid cuboid has a volume of 40 cm³. The cuboid has a total surface area of 100 cm squared. One edge of the cuboid has a length of 2 cm. Find the length of a diagonal of the cuboid. Give your answer correct to 3 sig. Fig. - Area of garden

If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas - The sides

The sides of the rectangle are in a ratio of 3: 5 and its circumference measures 72 cm. Calculate: a) the size of both sides of the rectangle b) the area of the rectangle c) the length of the diagonals - Isosceles triangle

The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area. - Garage

There are two laths in the garage opposite one another: one 2 meters long and the second 3 meters long. They fall against each other and stay against the opposite walls of the garage and both laths cross 70 cm above the garage floor. How wide is the garag - Isosceles trapezoid

Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high. - Three shapes

1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?

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