Area of shape - high school - 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: 267

Pipeline
How much percent has changed (reduced) area of pipe cross-section, if circular shape changed to square with same perimeter?
Annular area
The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
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.
Interesting property
Plot a rectangular shape has the interesting property that circumference in meters and the area in square meters are the same numbers. What are the dimensions of the rectangle?
The funnel
The funnel has the shape of an equilateral cone. Calculate the content of the area wetted with water if you pour 3 liters of water into the funnel.
Airplane
Aviator sees part of the earth's surface with an area of 200,000 square kilometers. How high he flies?
The plaster cast
The plaster cast has the shape of a regular quadrilateral pyramid. The cover consists of four equilateral triangles with a 5 m side. Calculate its volume and surface area.
The farmer
The farmer would like to first seed his small field. The required amount depends on the seed area. Field has a triangular shape. The farmer had fenced field, so he knows the lengths of the sides: 119, 111 and 90 meters. Find a suitable way to determine th
Inscribed rectangle
The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
Quatrefoil
Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
Pentagon
Calculate the area of a regular pentagon, which diagonal is u=17.
Two rectangles 2
A square of area 36 cm² is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.
Rectangle - area, perimeter
The area of a rectangular field is equal to 300 square meters. Its perimeter is equal to 70 meters. Find the length and width of this rectangle.
The roof
The roof has the shape of a spherical canopy with a base diameter of 8 m and a height of 2 m, calculate the area of the foil with which the roof is covered, when we calculate 13% for waste and residues.
Equilateral triangle v2
Equilateral triangle has a perimeter 36 dm. What is its area?
Squaring the Circle
Calculating side of the square with the same area as the circle of radius 18.
Hexagon
There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
Rhombus
The rhombus with area 68 has one diagonal is longer by 6 than second one. Calculate the length of the diagonals and rhombus sides.
Triangle
Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
Triangle SSS
Calculate perimeter and area of a triangle ABC, if a=53, b=46 and c=40.

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