# Planimetrics - math word problems

Study plane measurements, including angles, distances, and areas. In other words - measurement and calculation of shapes in the plane. Perimeter and area of plane shapes.

#### Number of problems found: 1947

• Coal mine
The towing wheel has a diameter of 1.7 meters. How many meters does the elevator cage lower when the wheel turns 32 times?
• Box
Calculate the angle between box base 9 x 14 and body diagonal length 18.
• Greatest angle
Calculate the greatest triangle angle with sides 197, 208, 299.
• Sum of inner angles
Prove that the sum of all inner angles of any convex n-angle equals (n-2) . 180 degrees.
• Square
Calculate the perimeter and the area of square with a diagonal length 30 cm.
• Grid/network of cube
Grid of cube has a circumference 42 mm. Calculate the surface area of the cube ...
• Circle
Write the equation of a circle that passes through the point [0,6] and touch the X-axis point [5,0]: ?
• Cable
Cable consists of 8 strands, each strand consists of 12 wires with diameter d = 0.5 mm. Calculate the cross-section of the cable.
• Triangle SSS
Calculate perimeter and area of ​​a triangle ABC, if a=53, b=46 and c=40.
• Right angle
If a, b and c are two sides of a triangle ABC, a right angle in A, find the value on each missing side. If b=10, c=6
• Isosceles trapezoid
Perimeter of the isosceles trapezoid is 48 cm. One side is two times greater than the second side. Determine the dimensions of the trapezoid.
• The central
The central angle of a sector is 30° and the radius is 15 m. Determine its perimeter.
• Body diagonal
Find the cube surface if its body diagonal has a size of 6 cm.
• Funnel
The funnel has the shape of an equilateral cone. Calculate the surface wetted with water if we poured into the funnel 7.1 liters of water.
• Equilateral triangle
Calculate the side of an equilateral triangle, if its area is 892 mm2.
• Triangular pyramid
What is the volume of a regular triangular pyramid with a side 3 cm long?
On a straight stretch of road is marked 12 percent drop. What angle makes the direction of the road with the horizontal plane?
• Semicircle
To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
• Pentagon
Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch.
• Estate
Semicircle estate must be fence. The straight section has 26 meters long fence. How many meters of fence should buy?

Do you have an interesting mathematical word problem that you can't solve it? Submit a math problem, and we can try to solve it.

We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...