Area of shape - 7th grade (12y) - 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: 248

Square gardens
The gardening colony with dimensions of 180 m and 300 m is to be completely divided into equally large square areas with the largest possible area. Calculate how many such square areas can be obtained and determine the side length of the square.
Gardens
The area of the square garden is 3/4 of the area of the triangular garden with sides of 80 m, 50 m, 50 m. How many meters of the fence do we need to fence a square garden?
Isosceles trapezoid
Find the area of an isosceles trapezoid with bases of 8cm and 72mm. The height of the trapezoid is equal to three-quarters of the longer base.
Hectares
Determine the area of the rectangular land (in ha), which has dimensions of 3 cm and 4.5 cm on the plan with a scale of 1: 40,000.
Height
The content of the triangle is 35 cm². The length of the base is 10 cm. Determine the length of the height on the base.
Cylinder container
The cylindrical container with a diameter of 1.8 m contains 2,000 liters of water. How high does the water reach?
The trench
Calculate how many cubic meters of soil needs to be removed from the excavation in the shape of an isosceles trapezoid, the top width is 3 meters, the lower width is 1.8 m, the depth of the excavation is 1 m, and the length is 20 m.
Largest wall
Find the content of the largest wall of a prism with the base of a rectangle which has a height of 4 dm, side c = 5 cm, and side b = 6 cm.
Quadrilateral prism
Calculate the surface of a quadrilateral prism according to the input: Area of the diamond base S1 = 2.8 m², length of the base edge a = 14 dm, height of the prism 1,500 mm.
Wooden box
The block-shaped box was placed on the ground, leaving a rectangular print with dimensions of 3 m and 2 m. When flipped over to another wall, a print with dimensions of 0.5 m and 3 m remained in the sand. What is the volume of the wooden box?
Quadrilateral prism
The surface of the regular quadrilateral prism is 8800 cm², the base edge is 20 cm long. Calculate the volume of the prism
Cutting the prism
A prism with a square base with a content of 1 cm² and a height of 3 cm was cut from a cube with an edge length of 3 cm. What is the surface of the body formed from the cube after cutting the prism?
Largest squares
How many of the largest square sheets did the plumber cut the honeycomb from 16 dm and 96 dm?
The hollow cylinder
The hollow cylinder has a height of 70 cm, an outer diameter of 180 cm and an inner diameter of 120 cm. What is the surface of the body, including the area inside the cavity?
Garden exchange
The garden has the shape of a rectangular trapezoid, the bases of which have dimensions of 60 m and 30 m and a vertical arm of 40 m. The owner exchanged this garden for a parallelogram, the area of which is 7/9 of the area of a trapezoidal garden. What is
Wallpaper
3750 cm square of wallpaper is needed to glue a cube-shaped box. Can Dad cut out the whole necessary piece of wallpaper as a whole if he has a roll of wallpaper 50 cm wide?
Height to the base
The triangle area is 35 cm ^ 2. The size of the base is 10 cm. Find the length of height to the base.
Parallerogram
In parallelogram ABCD is a = 2.5 cm and height to side a is 7.2 cm and height to side b is 4 cm. Find the side length b.
Cross five
The figure on the picture is composed of the same squares and has a content of 45cm². What's its perimeter?
Perimeter of the circle
Calculate the perimeter of the circle in dm, whose radius equals the side of the square containing 0.49 dm²?

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