Planimetry - practice problems
The planimetrics studies plane measurements, including angles, distances, and areas. In other words, it involves the measurement and calculation of shapes in a two-dimensional plane. Typical problems include finding the perimeter and area of plane shapes.Planimetry is a subfield of geometry that focuses exclusively on plane figures (circles, triangles, quadrilaterals) and their:
- Mutual positions (perpendicularity, parallelism),
- Metric properties (circumference, area),
- Construction tasks (using compasses and ruler).
Example:
- Planimetry: Calculation of the area of a circle S = π r2 .
- Stereometry: Calculation of the volume of a sphere V = 43π r3 .
Planimetry is therefore a part of geometry that is limited to two-dimensional figures.
Number of problems found: 1437
- Piece of land
A farmer has a piece of land in the shape of a parallelogram. The two adjacent sides measure 15 metres and 10 metres. How much fencing is needed to enclose the entire plot? - Triangle - same sides
Can the sides of a triangle have lengths of 11, 11, and 14? If so, what type of triangle is it? - Circular pizza
A circular pizza has a radius of 6 inches. What is the approximate circumference of the pizza? (Use π = 3.14) - Polygon with x
All lines in the picture are perpendicular. Find the perimeter of the given polygon. - The length 19
The length and width of a rectangle are 1/6 inches and 3/8 inches. What is the perimeter (in inches) of the rectangle? - Regular hexagon
Calculate the perimeter of a regular hexagon with each side 5 cm. - A rectangular 12
A rectangular mobile phone has a length of 13 1/3 cm and a width of 5 1/3 cm. What is the perimeter of the phone? - Garden 39
Elina's garden has 5 sides. Each side is 8 m long. How many meters of fencing material does she need around the garden? - Garden hose
Miguel wound a garden hose around a circular real. If the diameter of the real is 10 inches, how many inches of hose was wound on the first full turn of the real round? The answer to the nearest whole inch, use 3.14 for pi. - The length 16
The length of a rectangle is 7.1 cm, and its breadth is 2.5 cm. What is the area of the rectangle? - A stop
A stop sign is in the shape of an 8-sided polygon (regular octagon) in which each side is 12 1/2 in. What is the perimeter? - The length 15
The length of the rectangle is twice as long as the width. The width is 104 cm. Find the perimeter of the rectangle. - The sides 7
The sides of the triangle are 5.2, 4.6, and x. If the PERIMETER of the triangle is 11.2 feet, what is the length of the unknown side? (hint: draw a picture) - One side 3
One side of a triangular banner is 1 1/2 times longer than the second side and 2 cm shorter than the third side. The perimeter of the triangle is 98 cm. How long is the shortest side? - General right triangle
In a right triangle, if a =x+34 and b = x and c= 50, then solve for x. Side c is a hypotenuse. Then discuss the case when a or b is a hypotenuse. - A rectangle 14 A rectangle is 8 cm long and 5 cm wide. Its perimeter is doubled when each of its sides is increased by x cm. From an equation in x, find the new length of the rectangle.
- The length 18 The length of a rectangle is three times its width. Suppose the perimeter is 96 cm. Calculate the width of the rectangle.
- The perimeter 10 The perimeter of a rectangle is 162 inches. The length is 35 inches longer than the width. Find the length and width of the rectangle.
- The hypotenuse
The hypotenuse of a right-angled triangle is 20 meters. If the difference between the lengths of the other sides is 4 meters, find the other sides. - Length and width
The length of a rectangle is 7 cm more than the width. Find the width and length if the perimeter of the rectangle is 78 cm.
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