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.

Number of problems found: 1802

  • Ratio of squares
    squares_cut_circles A circle is given in which a square is inscribed. The smaller square is inscribed in a circular arc formed by the side of the square and the arc of the circle. What is the ratio of the areas of the large and small squares?
  • Two gardens
    garden The total area of the two gardens is 864 m2. The first garden is 60 m2 smaller than three times the second garden. What is the area of each garden?
  • In the
    rectangle_1 In the rectangle ABCD, the distance of its center from the line AB is 3 cm greater than from the line BC. The circumference of the rectangle is 52 cm. Calculate the contents of the rectangle. Express the result in cm2.
  • Outside tangents
    tangent_circles Calculate the length of the line segment S1S2 if the circles k1 (S1, 8cm) and k2 (S2,4cm) touch the outside.
  • Length of the arc
    obluk What is the length of the arc of a circle k (S, r=68mm), which belongs to a central angle of 78°?
  • Similarity coefficient
    triangles In the triangle TMA the length of the sides is t = 5cm, m = 3.5cm, a = 6.2cm. Another similar triangle has side lengths of 6.65 cm, 11.78 cm, 9.5 cm. Determine the similarity coefficient of these triangles and assign similar sides to each other.
  • The diameter
    circles The diameter of a circle is 4 feet. What is the circle's circumference?
  • Bisectors
    right_triangle As shown, in △ ABC, ∠C = 90°, AD bisects ∠BAC, DE⊥AB to E, BE = 2, BC = 6. Find the perimeter of triangle △ BDE.
  • Interior angles
    triangles_1 Calculate the interior angles of a triangle that are in the ratio 2: 3: 4.
  • Half of halves
    sequence_geo Half of the square we cut off, then half of the rest, etc. Five cuts we made in this way. What part of the content of the original square is the content of the cut part?
  • Trip with compass
    compass2 During the trip, Peter went 5 km straight north from the cottage, then 12 km west and finally returned straight to the cottage. How many kilometers did Peter cover during the whole trip?
  • Central angle
    obluk What is the length of the arc of a circle with a diameter of 46 cm, which belongs to a central angle of 30°?
  • Flakes
    kvietok_MO A circle was described on the square, and a semicircle above each side of the square was described. This created 4 "flakes". Which is bigger: the content of the central square or the content of four chips?
  • Similar triangles
    triangles_1 In the triangle DEF is DE = 21cm, EF = 14.7cm, DF = 28cm. The triangle D´E´F´ is similar to the triangle DEF. Calculate the lengths of the sides of the triangle D´E´F´ if the similarity coefficient is one-seventh.
  • Diamond area from diagonals
    kosostvorec In the diamond ABCD is AB = 4 dm and the length of the diagonal is 6.4 dm long. What is the area of the diamond?
  • Fighter
    vyskovy uhol A military fighter flies at an altitude of 10 km. From the ground position, it was aimed at an altitude angle of 23° and 12 seconds later at an altitude angle of 27°. Calculate the speed of the fighter in km/h.
  • Two sides paint
    painter The door has the shape of a rectangle with dimensions of 260cm and 170cm. How many cans of paint will be needed to paint this door if one can of paint cover 2m2 of the area? We paint the doors on both sides.
  • Powerplant chimney
    komin2 From the window of the building at a height of 7.5 m, the top of the factory chimney can be seen at an altitude angle of 76° 30 ′. The base of the chimney can be seen from the same place at a depth angle of 5° 50 ′. How tall is the chimney?
  • Semicircle
    semicircles_rect Calculate the length of a semicircle with a radius of 6cm.
  • Concentric circles and chord
    tetiva2 In a circle with a diameter d = 10 cm, a chord with a length of 6 cm is constructed. What radius have the concentric circle while touch this chord?

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