# 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. Ellipse Ellipse is expressed by equation 9x2 + 25y2 - 54x - 100y - 44 = 0. Find the length of primary and secondary axes, eccentricity, and coordinates of the center of the ellipse.
2. 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?
3. The pond We can see the pond at an angle 65°37'. Its end points are 155 m and 177 m away from the observer. What is the width of the pond?
4. A map A map of size 60cm by 25cm is reduced in the ratio of 3:5, twice. What are the new dimensions?
5. Area of garden If the width of the rectangular garden is decreased by 2 meters and its length is increased by 5 meters, the area of the rectangle will be 0.2 ares larger. If the width and the length of the garden will increase by 3 meters, its original size will increas
6. 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.
7. The sides 2 The sides of a trapezoid are in the ratio 2:5:8:5. The trapezoid’s area is 245. Find the height and the perimeter of the trapezoid.
8. Diamond diagonals Find the diamond diagonal's lengths if the area is 156 cm2 and side is 13 cm long.
9. Nonagon Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
10. Right triangle Calculate the length of the remaining two sides and the angles in the rectangular triangle ABC if a = 10 cm, angle alpha = 18°40'.
11. Each with each Five pupils from 3A class played table tennis. How many matches did they play with each other?
12. Ratio of sides 2 The ratio of the side lengths of one square to another is 1:2. Find the ratio of the area of the two squares.
13. Rectangles The perimeter of a rectangle is 90 m. Divide it into three rectangles, the shorter side has all three rectangles the same, their longer sides are three consecutive natural numbers. What is the dimensions of each rectangle?
14. Is right triangle or not If right triangle ABC, have sides a=13, b=11.5, c=22.5. Find area. A meter pole perpendicular to the ground throws a shadow of 40 cm long, the house throws a shadow 6 meters long. What is the height of the house? Find radius of circle using pythagorean theorem where a=9, b=r, c= 6+r
17. Triangle perimeter Calculate the triangle perimeter whose sides are in ratio 3: 5: 7 and the longest side is 17.5 cm long.
18. Three points 2 The three points A(3, 8), B(6, 2) and C(10, 2). The point D is such that the line DA is perpendicular to AB and DC is parallel to AB. Calculate the coordinates of D.
19. Diagonals of a rhombus 2 One diagonal of a rhombus is greater than other by 4 cm . If the area of the rhombus is 96 cm2, find the side of the rhombus.
20. Construct Construct a rhombus ABCD, if the size of the diagonal AC is 6 cm and diagonal BD 8 cm long.

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