# 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

• Tree trunk From the tree trunk, the diameter at the narrower end is 28 cm, a beam of square cross-section is to be made. Calculate the longest side of the largest possible square cross-section.
• Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
• The perimeter The perimeter of equilateral △PQR is 12. The perimeter of regular hexagon STUVWX is also 12. What is the ratio of the area of △PQR to the area of STUVWX?
• 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.
• Two diagonals The rhombus has a side length 12 cm and length of one diagonal 21 cm. What is the length of the second diagonal?
• 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 mm2. 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.
• Cylinder - h Cylinder volume is 215 cm3. Base radius is 2 cm. Calculate the height of the cylinder.
• 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 cm2.
• Diamond and diagonals A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!) The regular quadrangular prism has a base edge a = 7.1 cm and side edge = 18.2 cm long. Calculate its volume and surface area.
• Height as diameter of base The rotary cylinder has a height equal to the base diameter and the surface of 471 cm2. Calculate the volume of a cylinder.
• Body diagonal The cuboid has a volume of 32 cm3. Its side surface area is double as one of the square bases. What is the length of the body diagonal?
• Square Points A[-9,7] and B[-4,-5] are adjacent vertices of the square ABCD. Calculate the area of the square ABCD.

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