Examples of area of plane shapes

Diagonal intersect
isosceles trapezoid ABCD with length bases | AB | = 6 cm, CD | = 4 cm is divided into 4 triangles by the diagonals intersecting at point S. How much of the area of the trapezoid are ABS and CDS triangles?
Two 2D shapes
Decide which shapes have more area: (a) a square of 8cm side; or (b) two rectangles with sides 5cm and 15cm? Write result as 1 or 2 (rectangles)
Perimeter of the circle
Calculate the perimeter of the circle in dm, whose radius equals the side of the square containing 0.49 dm²?
Octagonal pyramid
Find the volume of a regular octagonal pyramid with height v = 100 and the angle of the side edge with the plane of the base is α = 60°.
Tetrahedral pyramid
Determine the surface of a regular tetrahedral pyramid when its volume is V = 120 and the angle of the sidewall with the base plane is α = 42° 30´.
Uboid volume
Calculate the cuboid volume if the walls are 30cm², 35cm², 42cm²
The schoolyard
The schoolyard had the shape of a square with an 11m side. The yard has been enlarged by 75 m² and has a square shape again. How many meters was each side of the yard enlarged?
Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
Mysterious area
The trapezoid ABCD is given. Calculate its area if the area of the DBC triangle is 27 cm².
Hexagon
Calculate the surface of a regular hexagonal prism whose base edge a = 12cm and side edge b = 3 dm.
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 t
The parabolic segment
The parabolic segment has a base a = 4 cm and a height v = 6 cm. Calculate the volume of the body that results from the rotation of this segment a) around its base b) around its axis.
Paint cans
How many paint cans do we need to paint the floor in two rooms with dimensions of 6.8m x 4.5m and 6m x3.8m? One can arefor 6m².
Irregular pentagon
A rectangle-shaped, 16 x 4 cm strip of paper is folded lengthwise so that the lower right corner is applied to the upper left corner. What area does the pentagon have?
Rectangles
How many different rectangles can be made from 60 square tiles of 1 m square? Find the dimensions of these rectangles.
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.
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?
Circular railway
The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
Flowerbed
We enlarge the circular flower bed, so its radius increased by 3 m. The substrate consumption per enlarged flower bed was (at the same layer height as before magnification) nine times greater than before. Determine the original flowerbed radius.
Square side
If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square?

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