# Planimetrics - 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.- Rhombus 29

One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus. - Diagonal to area

Calculate the area of a rectangle in which the length of the diagonal is 10 cm. - Map scale

The rectangular plot has in a scale of 1: 10000 area 3 cm^{2}on the map. What content does this plot have on a 1:5000 scale map? - Painters

Six of the painters paint 90 m of fence in five hours. For how long would the 4 painters paint a 45 meter fence? How many meters fence painted painters 5 for two hours? - Three points 2

The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D. - A rectangular

A rectangular garden 40 m long and 30 m wide is to be fenced with fence posts at each corner. All the other posts will be 5 meters a part. How many posts will be needed to fence in the garden. - Perimeter of a rectangle

If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width? - Complementary angles 2

Two complementary angles are (x+4) and (2x - 7) find the value of x - Equilateral triangle

A square is inscribed into an equilateral triangle with a side of 10 cm. Calculate the length of the square side. - Ruler and compass

Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°. - Coordinate axes

Determine the area of the triangle given by line -7x+7y+63=0 and coordinate axes x and y. - Trapezoid - intersection of diagonals

In the ABCD trapezoid is AB = 8 cm long, trapezium height 6 cm, and distance of diagonals intersection from AB is 4 cm. Calculate trapezoid area. - Construct

Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long. - Sum of squares

The sum of squares above the sides of the rectangular triangle is 900 cm^{2.}Calculate content of square over the triangle's hypotenuse. - Table

Find the circumference of the table, where the long side is 1.28 meters and the short side is 86 cm. - Rectangle area

The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle? - Inscribed circle

Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC. - ABCD square

In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment? - Bamboo

Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken? - Two forces

The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.

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