Area + system of equations - practice problems - page 3 of 7
Number of problems found: 121
- Area and perimeter of rectangle
The rectangle area is 3000 cm2, and one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle. - Dimensions of the trapezoid
One of the trapezoid bases is one-fifth larger than its height, and the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm2 - Equation of the circle
Find the equation of the circle inscribed in the rhombus ABCD where A[1, -2], B[8, -3], and C[9, 4]. - Sow barley
Farmers wanted to sow barley within 13 days. Due to the excellent weather, they exceeded the daily plan of sowing by 2 ha and therefore finished sowing grain in 12 days. How many hectares of land did they sow with barley? - In the
In the rectangle ABCD, the distance of its center from line AB is 3 cm greater than from line BC. The circumference of the rectangle is 52 cm. Calculate the area of the rectangle. Express the result in cm². - Coordinates
Determine the coordinates of the vertices and the area of the parallelogram, the two sides of which lie on the lines 8x + 3y + 1 = 0, 2x + y-1 = 0 and the diagonal on the line 3x + 2y + 3 = 0 - The circumference
The circumference and width of the rectangle are in a ratio of 5:1. Its area is 216cm². What is its length? - Side lengths
In the triangle ABC, the height to side a is 6cm. The height to side b is equal to 9 cm. Side "a" is 4 cm longer than side "b". Calculate the side lengths a, b. - An equilateral
An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle? - wheat 20833
Mr. Vávra sows wheat and rye for a total of 28 ha. Rye sows two and a half times the area of wheat. How many ha sow wheat and how much rye? - Bent scale
Monica weighed 52 kg. Sara 54 kg. Together they weighed 111 kg. They noticed that the needle on the scale was bent. How much did they really weigh? - Block or cuboid
The wall diagonals of the block have sizes of √29cm, √34cm, and √13cm. Calculate the surface and volume of the block. - 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? - Czechoslovakia 17233
Slovakia has an area 38% smaller than the Czech Republic. Original Czechoslovakia had an area of 128,000 square kilometers. What are the areas of both states? - Three faces of a cuboid
The diagonal of the 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 simultaneously had an area of 40cm² and a circumference of 30cm. One of the patches was 8cm wide. What was the width of the sec - 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 enlarged 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. - Calculate 9701
In the triangle, the side length AB = 6 cm, the height per side c = 5 cm, and the angle BCA = 35°. Calculate sides a b.
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