# 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: 1973

- Angles of elevation

From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of - Axial section

Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder. - Axial section

The axial section of the cylinder has a diagonal 31 cm long, and we know that the area of the side and the base area is in ratio 3:2. Calculate the height and radius of the cylinder base. - Triangular pyramid

Determine the volume and surface area of a regular triangular pyramid having a base edge a=20 cm and a lateral edge b = 35 cm - Pyramid

Cuboid ABCDEFGH has dimensions AB 3 cm, BC 4 cm, CG 5 cm. Calculate the volume and surface area of a triangular pyramid ADEC. - Truncated pyramid

The concrete pedestal in the shape of a regular quadrilateral truncated pyramid has a height of 12 cm, the pedestal edges have lengths of 2.4 and 1.6 dm. Calculate the surface of the base. - 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}. - Cylinder surface, volume

The area of the cylinder surface and the cylinder jacket are in the ratio 3: 5. The height of the cylinder is 5 cm shorter than the radius of the base. Calculate surface area and volume of the cylinder. - Right circular cone

The volume of a right circular cone is 5 liters. Calculate the volume of the two parts into which the cone is divided by a plane parallel to the base, one-third of the way down from the vertex to the base. - House roof

The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m^{2}is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof? - The hall

The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m^{2}. What were the original dimensions of the hall? - Tangent 3

In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm. - Garden exchange

The garden has the shape of a rectangular trapezoid, the bases of which have dimensions of 60 m and 30 m and a vertical arm of 40 m. The owner exchanged this garden for a parallelogram, the area of which is 7/9 of the area of a trapezoidal garden. What is - Triangular prism

Calculate the surface of a triangular prism 10 cm high, the base of which is a triangle with sides 6 cm 8 cm and 8 cm - Truncated cone

A truncated cone has a bases radiuses 40 cm and 10 cm and a height of 25 cm. Calculate its surface area and volume. - Extending square garden

Mrs. Petrová's garden had the shape of a square with a side length of 15 m. After its enlargement by 64 m^{2}(square), it had the shape of a square again. How many meters has the length of each side of the garden been extended? - A map

A map with a scale of 1: 5,000 shows a rectangular field with an area of 18 ha. The length of the field is three times its width. The area of the field on the map is 72 cm square. What is the actual length and width of the field? - A concrete pedestal

A concrete pedestal has a shape of a right circular cone having a height of 2.5 feet. The diameter of the upper and lower bases are 3 feet and 5 feet, respectively. Determine the lateral surface area, total surface area, and the volume of the pedestal. - Circle section

Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector and

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