# 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.- Rhombus diagonal

Area of rhombus is 224. One diagonal measures 33, find length of other diagonal. - Chord - TS

The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS? - Isosceles IV

In an isosceles triangle ABC is |AC| = |BC| = 13 and |AB| = 10. Calculate the radius of the inscribed (r) and described (R) circle. - EQL triangle

Calculate inradius and circumradius of equilateral triangle with side a=77 cm. - Trapezoid ABCD v2

Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm^{2}. What is the area of trapezoid ABCD? - Flowerbed 2

Around the square flower bed in a park is sidewalk 2 m wide. The area of this sidewalk is 243 m^{2}. What is the area of the flowerbed? - Bases

The length of the bases trapezium are in ratio 4:5. Length of midline is 15. How long are the bases of a trapezoid? - Circle

Circle is given by centre on S[-7; 10] and maximum chord 13 long. How many intersect points have circle with the coordinate axes? - Flowerbed

Flowerbed has the shape of an isosceles obtuse triangle. Arm has a size 5.5 meters and an angle opposite to the base size is 94°. What is the distance from the base to opposite vertex? - Round table

Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes? - Semicircle

In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC? - Cable car 2

Cable car rises at an angle 41° and connects the upper and lower station with an altitude difference of 1175 m. How long is the track of cable car? - Trapezoid ABCD

Calculate the perimeter of trapezoid ABCD if we know the side c=15, b=19 which is also a height and side d=20. - Circle section

Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector - The bridge

Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle? - Sector

The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes. - Hexagon A

Calculate area of regular hexagon inscribed in circle with radius r=9 cm. - Arc

The length of the circle is 41 amd arc length of the circle 9. What is the magnitude of the angle of this arc? - RT 10

Area of right triangle is 84 cm^{2}and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC. - Rectangles - sides

One side of the rectangle is 10 cm longer than second. Shortens longer side by 6 cm and extend shorter by 14 cm increases the area of the rectangle by 130 cm^{2}. What are the dimensions of the original rectangle?

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