# 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.- Children playground

The playground has the shape of a trapezoid, the parallel sides have a length of 36 m and 21 m, the remaining two sides are 14 m long and 16 m long. Determine the size of the inner trapezoid angles. - Diagonals

What x-gon has 54 diagonals? - The pole

The telegraph pole is supported by a 4 m bullet at 3/4 of its height, the end of which is at a distance 2.5 m from the pole post. Calculate the height of the telegraph pole. - Trapezium 2

Trapezium has an area of 24 square cms. How many different trapeziums can be formed ? - Hyperbola

Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - Pendulum

Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm. - Clock hands

The second hand has a length of 1.5 cm. How long does the endpoint of this hand travel in one day? - Vertices of a right triangle

Show that the points D(2,1), E(4,0), F(5,7) are vertices of a right triangle. - Cross road

From the junction of two streets that are perpendicular to each other, two cyclists (each on another street) walked out. One ran 18 km/h and the second 24 km/h. How are they away from a) 6 minutes, b) 15 minutes? - Rhombus 29

One of the diagonals of a rhombus is equal to a side of the rhombus. Find the angles of the rhombus. - 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. - Pravoúhly trojúhelník

Určete obsah pravoúhlého trojúhelníku, jehož délky stran tvoří po sobě jdoucí členy aritmetické posloupnosti a poloměr kružnice opsané tomuto trojúhelníku je 5 cm. - Isosceles triangle

The leg of the isosceles triangle is 5 dm, its height is 20 cm longer than the base. Calculate base length z. - A trapezoid

A trapezoid 75 ft wide on top 85 ft on the bottom, the height is 120 ft. What is its area in the square yds? - Right angled triangle 3

Side b = 1.5, hypotenuse angle A = 70 degrees, Angle B = 20 degrees. Find its unknown sides length. - Scale of plan

On the plan of the village in the scale of 1: 1000 a rectangular garden is drawn. Its dimensions on the plan are 25mm and 28mm. Determine the area of the garden in ares. - Rectangle

There is a rectangle with a length of 12 cm and a diagonal 8 cm longer than the width. Calculate the area of rectangle. - RT sides

Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm. - Table

Find the circumference of the table, where the long side is 1.28 meters and the short side is 86 cm. - Tangent 3

In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.

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