# 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: 2106

- Minute hand

What is the distance the minute hand of the clock travels in 12 minutes, if the diameter of the clock is 30 cm and the hand extends to a distance of 2 cm from the edge of the clock? - Regular 4-sided pyramid

Find the area (surface area) of a regular 4-sided pyramid if its height is 20 m and the wall height is 23 m. - Trapezoid - hard example

Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter. - Regular square prism

The volume of a regular square prism is 192 cm^{3}. The size of its base edge and body height are 1: 3. Calculate the surface of the prism. - Rectangular

Rectangular triangle KLM with right angle at vertex L, angle beta at vertex K and angle alpha at vertex M. Angle at vertex M = 65°, side l = 17.5 cm. Use Pythagorean theorems and trigonometric functions to calculate the lengths of all sides and the angle - Circular segment

Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ) - Rectangular field

A rectangular field has a diagonal of length 169m. If the length and width are in the ratio 12:5. Find the dimensions of the field, the perimeter of the field and the area of the field. - 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 - Two parallel chords

In a circle 70 cm in diameter, two parallel chords are drawn so that the center of the circle lies between the chords. Calculate the distance of these chords if one of them is 42 cm long and the second 56 cm. - Area and two angles

Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°. - Arc and segment

Calculate the length of circular arc l, area of the circular arc S_{1}and area of circular segment S_{2}. Radius of the circle is 11 and corresponding angle is ?. - Rectangular garden

Rectangular garden has a length of 48.7 m, a width of 6.3 meters shorter than the length. How much mesh should be bought for its fencing if the gate is 2.9 m long and the gate 1.1 m? What is the area of the garden? - Two gardens

The flower garden has a square shape. The new garden has the shape of a rectangle, and one dimension is 8 m smaller, and the other is twice as large as in a square garden. What were the original garden dimensions and the new garden if both gardens' area i - An observer

An observer standing west of the tower sees its top at an altitude angle of 45 degrees. After moving 50 meters to the south, he sees its top at an altitude angle of 30 degrees. How tall is the tower? - The bases

The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid. - 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? - 4side pyramid

Calculate the volume and surface of 4 sides regular pyramid whose base edge is 4 cm long. The angle from the plane of the sidewall and base plane is 60 degrees. - Plastic pipe

Calculate the plastic pipe's weight with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m^{3}. - Isosceles triangle

The perimeter of an isosceles triangle is 112 cm. The length of the arm to the length of the base is at ratio 5:6. Find the triangle area. - Plot

The length of the rectangle is 8 smaller than three times the width. If we increase the width by 5% of the length and the length is reduced by 14% of the width, the circumference of rectangle will be increased by 30 m. What are the dimensions of the recta

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