Area of shape + system of equations - math problems

Area is the quantity that expresses the extent of a two-dimensional shape. The area can be understood as the amount of paint necessary to cover the surface with a single coat. The area of a shape can be measured by comparing the shape to squares of a fixed size 1 m^2 or 1 cm^2 etc. Every unit of length has a corresponding unit of area. Areas can be measured in square metres (m^2), square centimetres (cm^2), square millimetres (mm^2), square kilometres (km^2), square feet (ft^2), square yards (yd^2), square miles (mi^2), and so forth.

Number of problems found: 38

Garden
The garden has a rectangular shape and has a circumference of 130 m and area 800.25 m². Calculate the dimensions of the garden.
Area and perimeter of rectangle
The content area of the rectangle is 3000 cm², one dimension is 10 cm larger than the other. Determine the perimeter of the rectangle.
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?
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?
Right triangle eq2
Find the lengths of the sides and the angles in the right triangle. Given area S = 210 and perimeter o = 70.
Rectangle - sides ratio
Calculate the area of a rectangle whose sides are in ratio 3:13 and perimeter is 673.
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?
Triangle ABC
Calculate the sides of triangle ABC with area 1404 cm² and if a: b: c = 12:7:18
AP RT triangle
The length of the sides of a right triangle form an arithmetic progression, longer leg is 24 cm long. What are the perimeter and area?
Trapezoid
How long are the trapezoid bases with area 24 cm² and height 3 cm. One base is 3 times longer than the shorter.
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?
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.
Trapezoid
trapezoid ABCD a = 35 m, b=28 m c = 11 m and d = 14 m. How to calculate its area?
The circumference
The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
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.
Circle arc
Circle segment has a circumference of 135.26 dm and 2096.58 dm² area. Calculate the radius of the circle and size of the central angle.
Two squares
Two squares whose sides are in the ratio 5:2 have a sum of its perimeters 73 cm. Calculate the sum of the area of these two squares.
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.
Two lands
The common area of the two neighboring lands is 964 m². The second land is 77 m² smaller than twice the size of the first land. Find the areas of each land.
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?