# 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

- Paper squares

The paper rectangle measuring 69 cm and 46 cm should be cut into as many squares as possible. Calculate the lengths of squares and their number. - Two squares

Two squares whose sides are in the ratio 5:2 have a sum of its perimeters 73 cm. Calculate the sum of the area of these two squares. - Common chord

Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles? - Round flowerbed

Around a round flowerbed with a diameter of 6 meters and I will make a sidewalk up to 0.5 meters wide. How much gravel is needed if the layer is to be 5 cm high? - Negative and postcard

The image on the negative has dimensions of 36x24 mm and is enlarged to a postcard format of 13.5x9 cm. In what proportion have the lengths increased? In what proportion has the image content increased? - Quadrangular pyramid

The regular quadrangular pyramid has a base length of 6 cm and a side edge length of 9 centimeters. Calculate its volume and surface area. - Chimney and tree

Calculate the height of the factory chimney, which casts a shadow 6.5 m long in the afternoon. At the same time, a 6 m high tree standing near it casts a shadow 25 dm long. - 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? - Two 2D shapes

Decide which shapes have more area: (a) a square of 8cm side; or (b) two rectangles with sides 5cm and 15cm? Write result as 1 or 2 (rectangles) - 30-60-90

The longer leg of a 30°-60°-90° triangle measures 5. What is the length of the shorter leg? - Seeds

The field has a rectangular shape with dimensions of 128 m and 350 m. How many kg of seed are needed for sowing if the 1 m^{2}will consume 25 g of seeds? - Train

The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance of the place from the station where you need to start to brake. - Brass sphere

Find the weight of a brass ball with an outer radius of 12 cm, a wall thickness of 20 mm if the density of the brass is 8.5 g/cm3. - RTriangle 17

The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs. - The bus stop

The bus stop waiting room has the shape of a regular quadrilateral pyramid 4 m high with a 5 m base edge. Calculate how many m^{2}roofing is required to cover the three walls of the sheathing, taking into account 40% of the additional coverage. - 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 ?. - Flower bed

The park has a rectangular flower bed with dimensions of 3.2m and 1.5m. How many rose bushes will we plant in the flower bed if 20 dm^{2}are needed for one bush? - Medians in right triangle

It is given a right triangle, angle C is 90 degrees. I know it medians t1 = 8 cm and median t2 = 12 cm. .. How to calculate the length of the sides? - Square prism

Calculate the volume of a foursided prism 2 dm high, the base is a trapezoid with bases 12 cm, 6 cm, height of 4 cm and 5 cm long arms. - Cutting paper

Divide a rectangular paper with dimensions 220mm and 308mm into squares of the same size so that they are as large as possible. Specify the length of the side of the square.

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