System of equations + area of a shape - practice problems - page 2 of 5
Number of problems found: 93
- Trapezoid 65644
In an isosceles trapezoid, the base ratio a / c = 9/7, arm b = 10 cm, height v = 8 cm. Calculate the area of the trapezoid in cm². - Increases 63204
If side b of the rectangle increases by 1 cm and the other side decreases by 4 cm at the same time, the area of the rectangle decreases by 48 cm². If side b increases by 2 cm and side ao decreases by 1 cm at the same time, the area of the rectangle increa - Sidewalk 63134
A 2m wide sidewalk is built around the circular fountain. The radii of the circles that delimit the path on both sides are 4:3. What area in square meters does this sidewalk occupy? - The ratio 7
The ratio of the sides of two squares is 4:5 if the sum of their areas is 180 cm². Find the sides of the two squares. - 144 steps
To get around the garden, we have to take 144 steps—eight steps less in width than in length. One step is five decimetres long. What are the dimensions of the garden? What are its perimeter and its area? - Louis
Louis wants to carpet the rectangular floor of his basement. The basement has an area of 5,120 square feet. The width of the basement is 4/5 its length. What is the length of Louis's basement? - Truncated pyramid
The truncated regular quadrilateral pyramid has a volume of 74 cm3, a height v = 6 cm, and an area of the lower base 15 cm² greater than the upper base's area. Calculate the area of the upper base. - Circumference 43531
A triangle with a circumference of 69 cm has one side three times shorter than the longest of them and the other 3 cm shorter than the longest of them. Find the area of the triangle. - Harry
Harry Thomson bought a large land in the shape of a rectangle with a circumference of 90 meters. He divided it into three rectangular plots. The shorter side has all three plots of equal length. Their longer sides are three consecutive natural numbers. Fi - Perpendicular 41811
Calculate the area of a right triangle whose longer perpendicular is six dm shorter than the hypotenuse and three dm longer than the shorter perpendicular. - 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? - Direction vector
The line p is given by the point P [- 0,5; 1] and the direction vector s = (1,5; - 3) determines: A) value of parameter t for points X [- 1,5; 3], Y [1; - 2] lines p B) whether the points R [0,5; - 1], S [1,5; 3] lies on the line p C) parametric equations - Railway embankment
The railway embankment section is an isosceles trapezoid, and the bases' sizes are in the ratio of 5:3. The arms have a length of 5 m, and the embankment height is 4.8 m. Calculates the size of the embankment section area. - 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]. - 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.
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