# 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: 1949

- Two lands

The common area of the two neighboring lands is 964 m^{2}. The second land is 77 m^{2}smaller than twice the size of the first land. Find the areas of each land. - Triangular pyramid

It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm^{3}. What is it content (surface area)? - Quadrilateral prism

Calculate the surface of a quadrilateral prism according to the input: Area of the diamond base S1 = 2.8 m^{2}, length of the base edge a = 14 dm, height of the prism 1,500 mm. - Edge of prism

The regular quadrilateral prism has a surface of 250 dm^{2}, its shell has a content of 200 dm^{2}. Calculate its leading edge. - Outer angles

The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C? - Road embankment

Road embankment has a cross section shape of an isosceles trapezoid with bases 5 m and 7 m, and 2 m long leg. How many cubic meters of soil is in embankment length of 1474 meters? - Cuboid - edges

The cuboid has dimensions in ratio 4: 3: 5, the shortest edge is 12 cm long. Find: (A) the lengths of the remaining edges, (B) the surface of the cuboid, (C) the volume of the cuboid - Support colum

Calculate the volume and surface of the support column that is shaped as perpendicular quadrangular prism whose base is a rhombus with a diagonals u1 = 102 cm u2 = 64 cm. Column height is 1. 5m. - Rectangle

The perimeter of the rectangle is 22 cm and content area 30 cm^{2}. Determine its dimensions, if the length of the sides of the rectangle in centimeters is expressed by integers. - In the

In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm^{2}. - Regular quadrangular pyramid

The height of the regular quadrangular pyramid is 6 cm, the length of the base is 4 cm. What is the angle between the ABV and BCV planes? - Triangular prism

The plane passing through the edge AB and the center of segment CC' of regular triangular prism ABCA'B'C', has an angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism. - Trench

The trench is a four-sided prism. The cross section has a trapezoidal shape with basements of 4m and 6m, the length of the trench is 30m. What is the depth of the trench if we dig 60,000 l of soil. - Rectangular base pyramid

Calculate an area of the shell of the pyramid with a rectangular base of 2.8 m and 1.4 m and height 2.5 meters. - Isosceles trapezoid

Calculate the content of an isosceles trapezoid whose bases are at ratio 5:3, the arm is 6cm long and it is 4cm high. - Round table

Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes? - Office

Office building was built in the shape of a regular hexagon inscribed in a circle with a radius of 12 m. The height of the walls is 7m. How much CZK cost plastering the walls of the building, if per 1 m square cost CZK 400? - Plan of the village

Plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality. - Acute triangle

In the acute triangle KLM, V is the intersection of its heights and X is the heel of height to the side KL. The axis of the angle XVL is parallel to the side LM and the angle MKL is 70°. What size are the KLM and KML angles? - The schoolyard

The schoolyard had the shape of a square with an 11m side. The yard has been enlarged by 75 m^{2}and has a square shape again. How many meters was each side of the yard enlarged?

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