Perimeter + area of shape - math problems

  1. The circumference
    rectangle The circumference and width of the rectangle are in a ratio of 5: 1. its area is 216cm2. What is its length?
  2. The hollow cylinder
    duty_valec The hollow cylinder has a height of 70 cm, an outer diameter of 180 cm and an inner diameter of 120 cm. What is the surface of the body, including the area inside the cavity?
  3. The bases
    rr_lichobeznik The bases of the isosceles trapezoid ABCD have lengths of 10 cm and 6 cm. Its arms form an angle α = 50˚ with a longer base. Calculate the circumference and content of the ABCD trapezoid.
  4. Carpet
    koberec How many crowns CZK do we pay for a carpet for a bedroom, when 1m of square carpet costs 350 CZK and the bedroom has dimensions of 4m and 6m? How many crowns do we pay for a strip around the carpet, when 1m of the strip costs 15 CZK?
  5. The playground
    playground The playground has the shape of a square with a side of 64 m. It is fenced on three sides. What is the area of the playground and how long is its fence?
  6. Triangular prism - regular
    prism3s The regular triangular prism is 7 cm high. Its base is an equilateral triangle whose height is 3 cm. Calculate the surface and volume of this prism.
  7. Horses playground
    kone_dzokej The fence for the horses has the shape of a rectangular trapezoid with an area of 400 m2, the base lengths should be 31 m and 19 m. How many meters of boards will they need to fence it if the boards are stacked in 5 rows?
  8. Triangular prism
    hranol3b The base of the perpendicular triangular prism is a rectangular triangle with a hypotenuse of 10 cm and one leg of 8 cm. The prism height is 75% of the perimeter of the base. Calculate the volume and surface of the prism.
  9. Squares ratio
    squares2 The first square has a side length of a = 6 cm. The second square has a circumference of 6 dm. Calculate the proportions of the perimeters and the proportions of the contents of these squares? (Write the ratio in the basic form). (Perimeter = 4 * a, conte
  10. Cross five
    5squares2 The figure on the picture is composed of the same squares and has a content of 45cm². What's its perimeter?
  11. Perimeter of the circle
    squares Calculate the perimeter of the circle in dm, whose radius equals the side of the square containing 0.49 dm2?
  12. Two patches
    krizik Peter taped the wound with two rectangular patches (one over the other to form the letter X). The area sealed with both patches at the same time had a content of 40cm2 and a circumference of 30cm. One of the patches was 8cm wide. What was the width of t
  13. Rectangular garden
    rectangle_1 The perimeter of Peter's rectangular garden is 98 meters. The width of the garden is 60% shorter than its length. Find the dimensions of the rectangular garden in meters. Find the garden area in square meters.
  14. Rectangle field
    land The field has a shape of a rectangle having a length of 119 m and a width of 19 m. , How many meters have to shorten its length and increase its width to maintain its area and circumference increased by 24 m?
  15. Circular railway
    described_circle2 The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
  16. Square side
    squares If we enlarge the square side a = 5m, its area will increase by 10,25%. How many percent will the side of the square increase? How many percent will it increase the circumference of the square?
  17. Calculate
    square Calculate the square area if its perimeter is 14dm.
  18. Squares
    squares2 From a square of 12 dm perimeter is cut smaller square, whose side is the third side of the square. What is the area of the rest?
  19. Area of a rectangle
    rectangle Calculate the area of a rectangle with a diagonal of u = 12.5cm and a width of b = 3.5cm. Use the Pythagorean theorem.
  20. 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.

Do you have an interesting mathematical word problem that you can't solve it? Submit math problem, and we can try to solve it.



We will send a solution to your e-mail address. Solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...