# 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

- The quadrilateral pyramid

The quadrilateral pyramid has a rectangular base of 24 cm x 3.2dm and a body height of 0.4m. Calculate its volume and surface area. - Rectangle diagonal

The rectangle, one side of which is 5 cm long, is divided by a 13 cm diagonal into two triangles. Calculate the area of one of these triangles in cm^{2}. - Moivre 2

Find the cube roots of 125(cos 288° + i sin 288°). - Round skirt

The cut on the round skirt has the shape of an annulus. Determine how much m² of fabric will be consumed on an 80 cm long skirt. The circumference of the waist is a circle with a smaller radius and is 69 cm. - Density of the concrete

Find the density of the concrete of the cuboid-shaped column has dimensions of 20 x 20 cm x 2 m if the weight of the column is 200 kg. - Regular triangular prism

Calculate the surface area of body of regular triangular prism, when the length of its base edge is 6.5 cm and height 0.2 m. - Tailor

Tailor has an estimated 11 meters of 80 cm wide fabric. He will shape wholly 7 rectangles measuring 80 x 150 cm and nothing fabric does not remain. How many fabric he have? - Metal tube

Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm^{3}of this metal is 9.5g. - Metal rails

Dad needs to improve the edges of the wooden boxes - to be reinforced with metal rails. How many cms of rails will he need if the box has the shape of a prism with the length of the edges 70cm 70cm and 120cm? - Similarity of squares

The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ? - The sides

The sides of the rectangle are in a ratio of 3: 5 and its circumference measures 72 cm. Calculate: a) the size of both sides of the rectangle b) the area of the rectangle c) the length of the diagonals - Outer contact of circles

Construct a circle k1 (S1; 1.5 cm), k2 (S2; 2 cm), and K3 (S3; 2.5 cm) so that they are always two outer contacts. Calculate the perimeter of the triangle S_{1}S_{2}S_{3}. - Powerplant chimney

From the building window at the height of 7.5 m, we can see the top of the factory chimney at an altitude angle of 76° 30 ′. We can see the chimney base from the same place at a depth angle of 5° 50 ′. How tall is the chimney? - Regular quadrilateral pyramid

Find the volume and surface of a regular quadrilateral pyramid if the bottom edge is 45 cm long and the pyramid height is 7 cm. - Iceberg

What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg? - 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)? - Equilateral cylinder

Equilateral cylinder (height = base diameter; h = 2r) has a volume of V = 199 cm^{3}. Calculate the surface area of the cylinder. - Alcohol from potatoes

In the distillery, 10 hl of alcohol can make from 8 t of potatoes. The rectangular field with dimensions of 600 m and 200 m had a yield of 20 t of potatoes per hectare. How many square meters of area are potatoes grown to obtain one liter of alcohol? - The tower

The observer sees the tower's base 96 meters high at a depth of 30 degrees and 10 minutes and the top of the tower at a depth of 20 degrees and 50 minutes. How high is the observer above the horizontal plane on which the tower stands? - Plot

The plot on which Mr. Kalous is to build a house has the shape of a rectangle. On a 1: 500 scale, its dimensions are 7cm and 5.5cm. Find out the dimensions of the plot. Calculate the parcel size.

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