# 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. Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
2. Segment in a triangle In a triangle ABC with the side/AB/ = 24 cm is constructed middle segment/DE/ = 18 cm parallel to the side AB at a distance 1 cm from AB. Calculate the height of the triangle ABC to side AB.
3. Inscribed circle XYZ is right triangle with right angle at the vertex X that has inscribed circle with a radius 5 cm. Determine area of the triangle XYZ if XZ = 14 cm.
4. Smallest internal angle Calculate what size has the smallest internal angle of the triangle if values of angles α:β:γ = 3:4:8
5. Rectangular trapezium Calculate the perimeter of a rectangular trapezium when its content area is 576 cm2 and sice a (base) is 30 cm, height 24 cm.
6. Angles of a triangle In the triangle ABC, the angle beta is 15° greater than the angle alpha. The remaining angle is 30° greater than the sum of the angles alpha and beta. Calculate the angles of a triangle.
7. Octagonal mat Octagonal mat formed from a square plate with a side of 40 cm so that every corner cut the isosceles triangle with leg 3.6 cm. What is the content area of one mat?
8. Clouds From two points A and B on the horizontal plane was observed forehead cloud above the two points under elevation angle 73°20' and 64°40'. Points A , B are separated by 2830 m. How high is the cloud?
9. Circle area Calculate the circle area with a radius of 1.2 m.
10. Is right triangle One angle of the triangle is 36° and the remaining two are in the ratio 3:5. Determine whether triangle is a rectangular triangle.
11. Tablecloth The table top is 90 cm long and 50 cm wide. How many cm lace edging is necessary for the tablecloth that hangs on each side by 10 cm?
12. Perimeter of circle Calculate the circumference of described circle to the triangle with sides 9,12,15 cm.
13. Percentage and rectangle About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%?
14. Trapezium ABCD In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60
15. Square - increased perimeter How many times is increased perimeter of the square, where its sides increases by 150%? If the perimeter of square will increase twice, how much% increases the content area of the square?
16. Tripled square If you tripled the length of the sides of the square ABCD you increases its content by 200 cm2. How long is the side of the square ABCD?
17. Triangle KLB It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area
18. Desribed circle to rectangle Rectangle with sides 6 cm and 4 cm was circumscribed circle. What part of the content of the circle determined by the circumscribed circle occupies a rectangle? Express in perctentages(%).
19. Rectangle The length of the rectangle are in the ratio 5:12 and the circumference is 238 cm. Calculate the length of the diagonal and area of rectangle.
20. Find the Find the radius of the circular base of the vessel, whose perimeter is 2.51 m. Write the result to one decimal place in meters. Via the π sign - Ludolph's number

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