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. Touch x-axis
    touch_circle Find the equations of circles that pass through points A (-2; 4) and B (0; 2) and touch the x-axis.
  2. The second
    triangle The second angle of a triangle is the same size as the first angle. The third angle is 12 degrees larger than the first angle. How large are the angles?
  3. Set of coordinates
    axes2 Consider the following ordered pairs that represent a relation. {(–4, –7), (0, 6), (5, –3), (5, 2)} What can be concluded of the domain and range for this relation?
  4. Three altitudes
    triangle_vysky A triangle with altitudes 4; 5 and 6 cm is given. Calculate the lengths of all medians and all sides in a triangle.
  5. Isosceles triangle 9
    iso_triangle Given an isosceles triangle ABC where AB= AC. The perimeter is 64cm and altitude is 24cm. Find the area of the isosceles triangle
  6. One side
    angle_incline One side is 36 long with a 15° incline. What is the height at the end of that side?
  7. The perimeter 3
    rectangles The perimeter of a rectangle is 35 cm. The ratio of the length to its width is 3:2. Calculate the dimensions of the rectangle
  8. Annular area
    medzikrucie2 The square with side a = 1 is inscribed and circumscribed by circles. Find the annular area.
  9. A kite
    kite2 ABCD is a kite. Angle OBC = 20° and angle OCD = 35°. O is the intersection of diagonals. Find angle ABC, angle ADC and angle BAD.
  10. A rectangular patio
    rectangles A rectangular patio measures 20 ft by 30 ft. By adding x feet to the width and x feet to the length, the area is doubled. Find the new dimensions of the patio.
  11. Ratio of sides
    described_circle2 Calculate the area of a circle that has the same circumference as the circumference of the rectangle inscribed with a circle with a radius of r 9 cm so that its sides are in ratio 2 to 7.
  12. Rectangular trapezoid
    rt_trapezium In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.
  13. A photograph
    photo A photograph will stick to a white square letter with a x cm length. The photo is 3/4 x cm long and 20 cm wide than the width of the paper. The surface of the remaining paper surrounding the photograph is 990 cm2. Find the size of paper and photo.
  14. Rectangular garden 2
    garden A farmer bought 600 m of wire for the fence. He wants to use it to besiege a rectangular garden with a surface of 16875 m2. Calculate the size of the garden.
  15. RT sides
    described_circle_right_triangle Find the sides of a rectangular triangle if legs a + b = 17cm and the radius of the written circle ρ = 2cm.
  16. Perimeter of RT
    triangle_rt1 Find the circumference of the rectangular triangle if the sum of its legs is 22.5 cm and its area is 62.5 cm2.
  17. Photo frame
    photo A square shape photo with a side length of 20 cm is framed by a 4 cm wide bar. Find the external frame size of this photo (the frame is from all sides)
  18. Concentric circles
    medzikruzie2 There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
  19. Percent change
    rectangles If the length of a rectangle is increased by 25% and the width is decreased by 10%, the area of the rectangle is larger than the area of the original rectangle by what percent?
  20. Diamond and diagonals
    kosostvorec A diamond has diagonals f = 8 cm and g = 6 cm long. How long is this diamond perimeter? (Calculate it!)

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