# 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.- Vertices of RT

Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle. - RT leg and perimeter

Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269. - 10 pieces

How to divide the circle into 10 parts (geometrically)? - Map scale

Garden has on plan on a scale of 1: 150 width 22 cm and length 35 cm. What is the real area of the garden? - Square room

What is the size of the smallest square room, which can pave with tiles with dimensions 55 cm and 45 cm? How many such tiles is needed? - Median

In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb. - Three shapes

1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle? - Inscribed triangle

To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle. - Cosine

The point (8, 6) is on the terminal side of angle θ. cos θ = ? - 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°. - 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? - Mine

Wheel in traction tower has a diameter 4 m. How many meters will perform an elevator cabin if wheel rotates in the same direction 89 times? - Orchard

Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the rou - Triangle

For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle? - Diameter

What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm? - Cutting circles

From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste? - Tree

How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground. - Semicircle

To a semicircle with diameter 10 cm inscribe square. What is the length of square sides? - Rhombus

ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. - Quadrilateral

In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm^{2}, what is the area of ABCD?

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See also more information on Wikipedia.