# 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. Circle's chords In the circle there are two chord length 30 and 34 cm. The shorter one is from the center twice than longer chord. Determine the radius of the circle.
2. The field The player crossed the field diagonally and walked the length of 250 m. Calculate the length of the field, circumference if one side of field 25 meters.
3. Sides of triangle Triangle has circumference 42 cm. Side a is 2 times shorter than side b and sice c is 2 cm longer than side a. Determine the sizes of sides of a triangle.
4. Square glass What is the area of the square window glass with the side 4 dm? Do you know how many cm2 is it?
5. Internal angles Find the internal angles of the triangle ABC if the angle at the vertex C is twice the angle at the B and the angle at the vertex B is 4 degrees smaller than the angle at the vertex A.
6. Rhumbline Find circumference and area of the rhumbline ABCD if the short side AD of which has a length of 5 cm, and the heel of the height from D leading to the AB side divides the AB side into two sections of 3 cm and 4 cm.
7. Trapezium The area of trapezium is 35 cm2. Find its altitude if the bases are 6cm and 8 cm.
8. Euclid theorems Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
9. Broken tree The tree is broken at 4 meters above the ground and the top of the tree touches the ground at a distance of 5 from the trunk. Calculate the original height of the tree.
10. Parabola 3 Find the equation of a parabola with its focus at (0,2) and its vertex at the origin. ?
11. Hall Rectangular hall will have pave by square tiles with a side length 15 cm. The hall has length 18 meters and width 3 m. How many tiles need to buy if 2 percent of the amount is disrupted during the work?
12. Sunflower Field The trapezoidal sunflower field is located between two parallel paths which are spaced 230 meters apart. The lengths of the parallel sides of the field are 255 m and 274 m. How many tons of sunflower will come from this field if the hectare yield is 2.25
13. A mast A mast 32 meters high was broken by the wind so that its top touches the ground 16 meters from the pole. The still standing part of the mast, the broken part and the ground form a rectangular triangle. At what height was the mast broken?
14. Rectangular triangle PQR In the rectangular triangle PQR, the PQ leg is divided by the X point into two segments of which longer is 25cm long. The second leg PR has a length 16 cm. The length of the RX is 20 cm. Calculate the length p of side RQ. The result is round to 2 decima
15. Circle tangent It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
16. Hectares The rectangular land is 350m long and 200m wide. Calculate the area in hectares.
17. RT perimeter The leg of the rectangular triangle is 7 cm shorter than the second leg and 8 cm shorter than the hypotenuse. Calculate the triangle circumference.
18. Rectangle from string String 12m. Make rectangle when one side is two times longer than its width.
19. Four sides of trapezoid Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.
20. Folded square ABCD is a square. The square is folded on the midpoint of AB and A is folded onto the fold, creating a shaded region. The perimiter of the shaded figure is 75. Find the area of square ABCD

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