# 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. Right isosceles triangle Right isosceles triangle has an altitude x drawn from the right angle to the hypotenuse dividing it into 2 equal segments. The length of one segment is 5 cm. What is the area of the triangle?
2. Two gardeners The garden with an area of 81 square meters was divided by two gardeners in a ratio of 4: 5. How much did the second gardener get more first?
3. Concentric circles There is given a circle K with a radius r = 8 cm. How large must a radius have a smaller concentric circle that divides the circle K into two parts with the same area?
4. Perimeter of a rectangle If the perimeter of a rectangle is 114 meters and the length is twice the width plus 6 meters, what are the length and width?
5. Two angles The triangles ABC and A'B'C 'are similar. In the ABC triangle, the two angles are 25° and 65°. Explain why in the triangle A'B'C 'is the sum of two angles of 90 degrees.
6. Rectangle area The length of a rectangle of x units is increased by 10% and its width of y units is increased by 15%. What is the ratio of the area of the old rectangle to the area if the new rectangle?
7. A large A large gear will be used to turn a smaller gear. The large gear will make 75 revolutions per minute. The smaller gear must make 384 revolutions per minute. Find the smallest number of teeth each gear could have. [Hint: Use either GCF or LCM. ]
8. Maria Maria has decided to plant grapes in the garden behind her house. His neighbor Ben has grown grapes successfully for a long time and has given Maria advice on how to plant vines. Ben told her to plant them 3 meters apart in rows that are also 3 meters apar
9. Area to perimeter Calculate circle circumference if its area is 254.34cm2 5 triangles + 1 square = how many sides in all
11. Medians 2:1 Median to side b (tb) in triangle ABC is 12 cm long. a. What is the distance of the center of gravity T from the vertex B? b, Find the distance between T and the side b.
12. Rectangular trapezoid In a rectangular trapezoid ABCD with right angles at vertices A and D with sides a = 12cm, b = 13cm, c = 7cm. Find the angles beta and gamma and height v.
13. A rectangular A rectangular garden 40 m long and 30 m wide is to be fenced with fence posts at each corner. All the other posts will be 5 meters a part. How many posts will be needed to fence in the garden.
14. Thomas Thomas lives 400 meters away from Samko, Robo from Thomas also 400 m and Samko from Robo 500. Anton lives 300 meters away from Robo further as Samko. How far away lives Anton from Rob?
15. 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.
16. Sandbox Sandbox has area of 32 sq ft and length of 4 1/2 ft. What is width of sandbox.
17. In a 2 In a thirteen sided polygon, the sum of five angles is 1274°, four of the eight angles remaining are equal and the other four are 18° less than each of the equal angles. Find the angles. .
18. Divide Divide area of rectangles with dimensions 32m and 10m by the ratio 7: 9. What area corresponds to a smaller section?
19. A triangle A triangle has an angle that is 63.1 other 2 are in ratio of 2:5 What are the measurements of the two angles?
20. A rectangle A rectangle has an area of 36 cm2. What could the length and width of rectangle be?

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