# 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. Calculate Calculate the square area if its perimeter is 14dm.
2. Two chords Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
3. Coal mine The towing wheel has a diameter of 1.7 meters. How many meters does the elevator cage lower when the wheel turns 32 times?
4. Angles of elevation From points A and B on level ground, the angles of elevation of the top of a building are 25° and 37° respectively. If |AB| = 57m, calculate, to the nearest meter, the distances of the top of the building from A and B if they are both on the same side of
5. An equilateral triangle The perimeter of an equilateral triangle is 33cm. How long is each side? Calculate the radius of the circle whose length is 107 cm larger than its diameter
7. Distance between 2 points Find the distance between the points (7, -9), (-1, -9)
8. Squares 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?
9. The Eiffel Tower The top of the Eiffel Tower is seen from a distance of 600 meters at an angle of 30 degrees. Find the tower height.
10. The tractor The tractor sows an average of 1.5 ha per hour. In how many hours does it sows a rectangular trapezoid field with the bases of 635m and 554m and a longer arm 207m? The ladder has a length of 3 m and is leaning against the wall, and its inclination to the wall is 45°. How high does it reach?
12. The cable car The cable car has a length of 3,5 kilometers and an angle of climb of 30 degrees. What is the altitude difference between Upper and Lower Station?
13. Company logo The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
14. Let x Let x represent one quantity. State what that quantity represents. Express the second quantity in terms of x. The length of the rectangle is 4 inches less than 8 times the width.
15. Depth angles At the top of the mountain stands a castle, which has a tower 30 meters high. We see the crossroad in the valley from the top of the tower and heel at depth angles of 32° 50 'and 30° 10'. How high is the top of the mountain above the crossroad
16. Area of a 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.
17. Two rectangles 2 A square of area 36 cm2 is cut out to make two rectangles. A and B The area of area A to area B is 2 : 1 Find the dimensions of rectangles A and B.
18. Chauncey Chauncey is building a storage bench for his son’s playroom. The storage bench will fit into the corner and against two walls to form a triangle. Chanuncy wants to buy a triangular shaped cover for the bench. If the storage bench is 2 1/2 ft. Along one
19. Tree trunk What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm?
20. RPM An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?

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