# 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.

1. 30-gon At a regular 30-gon the radius of the inscribed circle is 15cm. Find the "a" side size, circle radius "R", circumference, and content area.
2. Map scale On a 1:1000 scale map is a rectangular land of 4.2 cm and 5.8 cm. What is the area of this land in square meters?
3. Sides od triangle Sides of the triangle ABC has length 4 cm, 5 cm and 7 cm. Construct triangle A'B'C' that are similar to triangle ABC which has a circumference of 12 cm.
4. Angles ratio The internal angles of a triangle are in ratio 1:4:5 What kind of triangle is it? (solve internal angles and write down and discuss)
5. Trapezoid How long are the trapezoid bases with area 24 cm2 and height 3 cm. One base is 3 times longer than the shorter.
6. V-belt Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm The shadow of the tree is 16 meters long. Shadow of two meters high tourist sign beside standing is 3.2 meters long. What height has tree (in meters)?
8. Center of gravity In the isosceles triangle ABC is the ratio of the lengths of AB and the height to AB 10:12. The arm has a length of 26 cm. If the center of gravity T of triangle ABC find area of triangle ABT.
9. Trapezoid MO-5-Z8 Trapezoid KLMN has bases 12 and 4 cm long. The area of triangle KMN is 9 cm2. What is the area of the trapezoid KLMN?
10. Circular segment Calculate the area S of the circular segment and the length of the circular arc l. The height of the circular segment is 2 cm and the angle α = 60°. Help formula: S = 1/2 r2. (Β-sinβ)
11. Trapezoid 15 Area of trapezoid is 266. What value is x if bases b1 is 2x-3, b2 is 2x+1 and height h is x+4
12. Isosceles right triangle Contents of an isosceles right triangle is 18 dm2. Calculate the length of its base.
13. Trapezoid thirds The ABCD trapezoid with the parallel sides of the AB and the CD and the E point of the AB side if the segment DE divides the trapezoid into two parts with the same area. Find the length of the AE line segment.
14. Rectangle Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width.
15. Diagonals Draw a square ABCD whose diagonals have a length of 6 cm
16. Equilateral triangle The equilateral triangle has a 23 cm long side. Calculate its content area. The double ladder shoulders should be 3 meters long. What height will the upper top of the ladder reach if the lower ends are 1.8 meters apart?
18. Rhombus If we increase the rhombus side by 2.4 cm; its perimeter is 20 cm. How long was the side of the rhombus?
19. Square Calculate the perimeter and the area of square with a diagonal length 30 cm.
20. Isosceles triangle Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.

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