# 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: 2136

- Shooter

The probability that a good shooter hits the center of the target circle I is 0.1. The probability that the target hit intercircle is II 0.58. What is the probability that it hits the target circle I or II? - Right triangles

How many right triangles we can construct from line segments 3,4,5,6,8,10,12,13,15,17 cm long? (Do not forget to the triangle inequality). - Garden

The garden has a rectangular shape with lengths of 25 and 40 meters. It has been expanded so that each of its size increased by one fifth. How many square meters increased its acreage? - Inscribed circle

Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC. - TV tower

Calculate the height of the television tower if an observer standing 430 m from the base of the tower sees the peak at an altitude angle of 23°? - Tereza

The cube has an area of base 256 mm^{2}. Calculate the edge length, volume, and area of its surface. - Triangular prism

Calculate the surface of a regular triangular prism, the edges of the base are 6 cm long and the height of the prism is 15 cm. - Rectangle - desc circle

Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter. - Depth angle

From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff? - Perimeter of RT

Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm^{2}. - Diamond and diagonals

A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!) - Spherical section cut

Find the volume of a spherical section if the radius of its base is 10 cm and the magnitude of the central angle ω = 120 degrees. - Concrete pedestal

The carpenters made wooden mold on a concrete pedestal in the shape of a cube with an edge 2 meters long. What is the area in which the concrete touches wooden molds? (No lid or bottom) - Body diagonal

The cuboid has a volume of 32 cm^{3}. Its side surface area is double as one of the square bases. What is the length of the body diagonal? - Draw triangle

Construct an isosceles triangle ABC, if AB = 7cm, the size of the angle ABC is 47°, arms | AC | = | BC |. Measure the size of the BC side in mm. - Trapezoid

How long are the trapezoid bases with area 24 cm^{2}and height 3 cm. One base is 3 times longer than the shorter. - Rectangles

Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm? - The diamond

The diamond has an area S = 120 cm^{2}, the ratio of the length of its diagonals is e: f = 5: 12. Find the lengths of the side and the height of this diamond. - Hexagonal pyramid

Find the volume of a regular hexagonal pyramid, the base edge of which is 12 cm long and the side edge 20 cm. - An equilateral

An equilateral triangle is inscribed in a square of side 1 unit long so that it has one common vertex with the square. What is the area of the inscribed triangle?

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