# 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

• Pyramid a+h
Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm.
• Boat
A force of 300 kg (3000 N) is required to pull a boat up a ramp inclined at 14° with horizontal. How much does the boat weight?
• Cable car
Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
• Equilateral triangle
A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side.
• An angle
An angle x is opposite side AB which is 10, and side AC is 15 which is hypotenuse side in triangle ABC. Calculate angle x.
• Drainage channel
The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel.
• Sails
We known heights 220, 165 and 132 of sail. It has triangular shape. What is the surface of the sail?
• Diagonals
Rhombus has two diagonals e=14 dm and f=11 dm. Calculate the side angle and height of the rhombus.
• Sides ratio
Calculate the circumference of a triangle with area 84 cm2 if a:b:c = 10:17:21
• The mast
A 40 m high mast is secured in half by eight ropes of 25 m long. The ends of the ropes are equidistant from each other. Calculate this distance.
• The field
The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
• Football field
The soccer field may have a width of 45 meters. This is 45 meters less than the length of the course. What can be the length of the football field?
• Curved surface area CSA
A cylinder 5cm high has a base radius(7/2) cm. Calculate the curved surface area.
• Rectangle
The rectangle has a perimeter 75 cm. Diagonal length is 32.5 cm. Determine the length of the sides.
• Two parallel chords
The two parallel chords of the circle have the same length of 6 cm and are 8 cm apart. Calculate the radius of the circle.
• The pot
Diameter of the pot 38 cm. The height is 30 cm. How many liters of water can fit in the pot?
• Circular motion
Mass point moves moves uniformly in a circle with radius r = 3.4 m angular velocity ω = 3.6 rad/s. Calculate the period, frequency, and the centripetal acceleration of this movement.
• Trapezoid ABCD
ABDC is a trapezoid in which AB and CD are parallel sides measuring 6 and 9 respectively. Angles ABC and BCD are both right angles. Find the length of segment BD.
• Arc
What area of a circle occupied the flowers planted in the arc of a circle with radius 4 m with central angle 45°?
• Inscribed circle
A circle is inscribed at the bottom wall of the cube with an edge (a = 1). What is the radius of the spherical surface that contains this circle and one of the vertex of the top cube base?

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...