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
    30gon 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
    rectangles_12 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
    podobnost 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
    triangles_16 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
    lichob_2_1 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
    remenice-a-remen1 Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
  7. Tree shadow
    tree3 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
    triangles_9 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
    lichobeznik-stredni_pricka_2 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
    odsek 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
    trapezoid3 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
    IsoscelesRightTriangle Contents of an isosceles right triangle is 18 dm2. Calculate the length of its base.
  13. Trapezoid thirds
    lichobeznik_mo_z8_3 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
    rectangles_11 Find the dimensions of the rectangle, whose perimeter is 108 cm and the length is 25% larger than the width.
  15. Diagonals
    stvorec_7 Draw a square ABCD whose diagonals have a length of 6 cm
  16. Equilateral triangle
    rs_triangle_1 The equilateral triangle has a 23 cm long side. Calculate its content area.
  17. Double ladder
    rr_rebrik 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
    kosostvorec_6 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
    ctverec_mo_2 Calculate the perimeter and the area of square with a diagonal length 30 cm.
  20. Isosceles triangle
    triangles_8 Calculate area and perimeter of an isosceles triangle ABC with base AB if a = 6 cm, c = 7 cm.

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