# 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. Inscribed circle Calculate the magnitude of the BAC angle in the triangle ABC if you know that it is 3 times less than the angle BOC, where O is the center of the circle inscribed in the triangle ABC.
2. ABCD square In the ABCD square, the X point lies on the diagonal AC. The length of the XC is three times the length of the AX segment. Point S is the center of the AB side. The length of the AB side is 1 cm. What is the length of the XS segment?
3. Bamboo Bamboo high 32 feet was at a certain height broken by the wind so the bamboo top reached the ground at a distance of 16 feet from the trunk. At what height from the ground was the bamboo broken?
4. Two forces The two forces F1 = 580N and F2 = 630N have the angle of 59 degrees. Calculate their resultant force F.
5. Tv screen The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
6. Right-angled triangle Determine the content of a right triangle whose side lengths form successive members of an arithmetic progression and the radius of the circle described by the triangle is 5 cm.
7. Garden The rectangular garden has dimensions of 27 m and 30 m. Peter and Katka split it in a ratio of 4:5. How many square meters did Katkin measure part of the garden?
8. Drawer The rectangular face of a drawer has a perimeter of 108 cm and a width of 18cm. Find the length and the area of the rectangular face of the drawer.
9. Two annuluses The area of the annular circle formed by two circles with a common center is 100 cm2. The radius of the outer circle is equal to twice the radius of the inner circle. Determine the outside circle radius in centimeters.
10. Diagonal he rectangular ABCD trapeze, whose AD arm is perpendicular to the AB and CD bases, has area 15cm square. Bases have lengths AB = 6cm, CD = 4cm. Calculate the length of the AC diagonal.
11. Pendulum Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.
12. Equation of circle 2 Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
13. Garden fence The garden has the shape of a rectangular triangle with an area of 96 square meters and a 16 m long one leg. How many meters of the fence need to be fenced?
14. The pole The telegraph pole is supported by a 4 m bullet at 3/4 of its height, the end of which is at a distance 2.5 m from the pole post. Calculate the height of the telegraph pole.
15. Endless lego set The endless lego set contains only 6, 9, 20 kilograms blocks that can no longer be polished or broken. The workers took them to the gym and immediately started building different buildings. And of course, they wrote down how much the building weighed. The
16. Sides of triangle Triangle circumference with two identical sides is 117cm. The third side measures 44cm. How many cms do you measure one of the same sides?
17. Clouds Approximately at what height is the cloud we see under an angle of 26°10' and see the Sun at an angle of 29°15' and the shade of the cloud is 92 meters away from us?
18. Clock hands The second hand has a length of 1.5 cm. How long does the endpoint of this hand travel in one day?
19. Diamond The diamond has a circumference of 48cm. Calculate the length of its side in dm.
20. Area of rectangle Calculate the area of rectangle in square meters whose sides have dimensions a = 80dm and b = 160dm.

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