# 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

- Floor

The floor area of the room is 31 m^{2}and has a width of 4.3 m. How many centimeters of circumference measured floor on the map at the scale 1:75? - Cuboid

Cuboid ABCDEFGH with 10 cm height has a base edge length 6 cm and 8 cm. Determine angle between body diagonal and the base plane (round to degrees). - Viewing angle

The observer sees a straight fence 60 m long at a viewing angle of 30°. It is 102 m away from one end of the enclosure. How far is the observer from the other end of the enclosure? - KLMN trapezoid

The KLMN trapezoid has bases KL 40cm and MN 16cm. On the KL base is point P. The segment NP divides the trapezoid into units with the same area. What is the distance of point P from point K? - Pyramid 4sides

Calculate the volume and the surface of a regular quadrangular pyramid when the edge of the base is 4 cm long and the height of the pyramid is 7 cm. - Sides of right angled triangle

One leg is 1 m shorter than the hypotenuse, and the second leg is 2 m shorter than the hypotenuse. Find the lengths of all sides of the right-angled triangle. - Right angled triangle

Hypotenuse of a right triangle is 17 cm long. When we decrease length of legs by 3 cm then decrease its hypotenuse by 4 cm. Determine the size of legs. - 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. - Isosceles trapezoid

What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm? - The pond

We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond? - Thales

Thales is 1 m from the hole. The eyes are 150 cm above the ground and look into the hole with a diameter of 120 cm as shown. Calculate the depth of the hole. - Rotation

The right triangle with legs 11 cm and 18 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone. - 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. - Orange and tangerine trees

Brad's father asked an engineer to survey the field behind their house. He wanted to plant some orange and tangerine trees there. According to the survey, the field is thirty-two feet long and six yards wide. What is the area of the field in sq feet? - Castle tower

The castle tower has a cone-shaped roof with a diameter of 10 meters and a height of 8 meters. Calculate how much m² of coverage is needed to cover it if we must add one-third for the overlap. - Sphere equation

Obtain the equation of sphere its centre on the line 3x+2z=0=4x-5y and passes through the points (0,-2,-4) and (2,-1,1). - Quadrangular prism

Calculate the volume and surface area of a regular quadrangular prism 35 cm high and the base diagonal of 22 cm. - Similarity coefficient

The triangles ABC and A "B" C "are similar to the similarity coefficient 2. The sizes of the angles of the triangle ABC are α = 35° and β = 48°. Find the magnitudes of all angles of triangle A "B" C ". - Rope

How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)? - Ladder

Adam placed the ladder of the house, the upper end reaching to the window at the height of 3.6m, and the lower end standing on level ground and was distant from a wall of 1.5m. What is the length of the ladder?

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