# 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. Annulus Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus.
2. Arc What area of a circle occupied the flowers planted in the arc of a circle with radius 4 m with central angle 45°?
3. Rectangle and circle The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long.
4. Euclid 5 Calculate the length of remain sides of a right triangle ABC if a = 7 cm and height vc = 5 cm.
5. Silver medal To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part?
6. Two forces Two forces with magnitudes of 25 and 30 pounds act on an object at angles of 10° and 100° respectively. Find the direction and magnitude of the resultant force. Round to two decimal places in all intermediate steps and in your final answer.
7. Circle sector Circular sector with a central angle 80 ° has area 1257 cm2. Calculate its radius r.
8. Clocks What distance will describe the tip of minute hand 6 cm long for 20 minutes when we know the starting position with finally enclose hands each other 120°?
9. Polygon 42 Which polygon has 42 more diagonals than sides?
10. RTriangle 17 The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs.
11. Clock face clock face is given. Numbers 10 and 5, and 3 and 8 are connected by straight lines. Calculate the size of their angles.
12. Circular lawn Around a circular lawn area is 2 m wide sidewalk. The outer edge of the sidewalk is curb whose width is 2 m. Curbstone and the inner side of the sidewalk together form a concentric circles. Calculate the area of the circular lawn and the result round to
13. Circle inscribed Calculate the perimeter and area of a circle inscribed in a triangle measuring 3 , 4 and 5 cm.
14. Inscribed triangle To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
15. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
16. Tailor Tailor has an estimated 11 meters of 80 cm wide fabric. He will shape wholly 7 rectangles measuring 80 x 150 cm and nothing fabric does not remain. How many fabric he have? 5 km long road begins at an altitude 500 meters above sea level and ends at a altitude 521 ASL. How many permille road rises?
18. Chord 3 What is the radius of the circle where the chord is 2/3 of the radius from the center and has a length of 10 cm?
19. Circular flowerbed Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle.
20. Acreage Plot has a diamond shape, its side is 25.6 m long and the distance of the opposite sides is 22.2 meters. Calculate its acreage.

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...