Examples of area of plane shapes

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: 748

Map scale
On a 1:1000 scale map is a rectangular land of 4.2 cm and 5.8 cm. What is the area of this land in square meters?
Right triangle eq2
Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
Triangle
Plane coordinates of vertices: K[11, -10] L[10, 12] M[1, 3] give Triangle KLM. Calculate its area and its interior angles.
Octagonal mat
Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat?
MO Z8–I–6 2018
In the KLMN trapeze, KL has a 40 cm base and an MN of 16 cm. Point P lies on the KL line so that the NP segment divides the trapezoid into two parts with the same area. Find the length of the KP line.
Octagonal tank
The tank has the shape of a regular octagonal prism without an upper base. The base edge has a = 3m, the side edge b = 6m. How much metal sheet is needed to build the tank? Do not think about losses or sheet thickness.
Squares above sides
Two squares are constructed on two sides of the ABC triangle. The square area above the BC side is 25 cm². The height vc to the side AB is 3 cm long. The heel P of height vc divides the AB side in a 2: 1 ratio. The AC side is longer than the BC side. Calc
Enlarged rectangle
The rectangle with dimensions of 8 cm and 12 cm is enlarged in a ratio of 5:4. What are the circumference and the area of the enlarged rectangle?
Diagonals at right angle
In the trapezoid ABCD, this is given: AB=12cm CD=4cm And diagonals crossed under a right angle. What is the area of this trapezoid ABCD?
The regular
The regular triangular prism has a base in the shape of an isosceles triangle with a base of 86 mm and 6.4 cm arms, the height of the prism is 24 cm. Calculate its volume.
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.
Cuboid box
How many m² paper is needed for the sticking cuboid box of dimensions 50 cm, 40 cm and 30 cm? To the folds add one-tenth the area.
Octagonal prism vase
0.7 l of water can be poured in an octagonal prism vase. What is the height of the vase, if the bottom has a area of 25 cm square and a thickness of 12 mm?
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 at the same time had a content of 40cm2 and a circumference of 30cm. One of the patches was 8cm wide. What was the width of the
Rectangular trapezium
Calculate the perimeter of a rectangular trapezium when its content area is 576 cm² and sice a (base) is 30 cm, height 24 cm.
Four circles
1) Calculate the circle radius if its area is 400 cm square 2) Calculate the radius of the circle whose circumference is 400 cm. 3) Calculate circle circumference if its area is 400 cm square 4) Calculate the circle's area if perimeter 400 cm.
Cuboid and eq2
Calculate the volume of cuboid with square base and height 6 cm if the surface area is 48 cm².
Which
Which of the following numbers most accurately area of a regular decagon with side s = 2 cm? (A) 9.51 cm² (B) 20 cm² (C) 30.78 cm² (D) 31.84 cm² (E) 32.90 cm²
Dimensions of the trapezoid
One of the bases of the trapezoid is one-fifth larger than its height, the second base is 1 cm larger than its height. Find the dimensions of the trapezoid if its area is 115 cm²
Square
Suppose the square's sides' length decreases by a 25% decrease in the content area of 28 cm². Determine the side length of the original square.

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