# 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. Vertices of RT Show that the points P1 (5,0), P2 (2,1) & P3 (4,7) are the vertices of a right triangle.
2. RT leg and perimeter Calculate the length of the sides of a right triangle ABC with hypotenuse c when the length of a leg a= 84 and perimeter of the triangle o = 269.
3. 10 pieces How to divide the circle into 10 parts (geometrically)?
4. Map scale Garden has on plan on a scale of 1: 150 width 22 cm and length 35 cm. What is the real area of the garden?
5. Square room What is the size of the smallest square room, which can pave with tiles with dimensions 55 cm and 45 cm? How many such tiles is needed?
6. Median In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
7. Three shapes 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
8. Inscribed triangle To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
9. Cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
10. Area and two angles Calculate the size of all sides and internal angles of a triangle ABC, if it is given by area S = 501.9; and two internal angles α = 15°28' and β = 45°.
11. Tailor Tailor has an estimated 11 meters of 80 cm wide fabric. He will shape wholly 7 rectangles measuring 80 x 150 cm and nothing fabric does not remain. How many fabric he have?
12. Mine Wheel in traction tower has a diameter 4 m. How many meters will perform an elevator cabin if wheel rotates in the same direction 89 times?
13. Orchard Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the rou
14. Triangle For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
15. Diameter What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
16. Cutting circles From the square 1 m side we have to cut the circles with a radius of 10 cm. How many discs we cut and how many percent will be waste?
17. Tree How tall is the tree that observed in the visual angle of 52°? If I stand 5 m from the tree and eyes are two meters above the ground.
18. Semicircle To a semicircle with diameter 10 cm inscribe square. What is the length of square sides?
19. Rhombus ABCD is a rhombus, ABD is an equilateral triangle and AC is equal to 4. Find the area of the rhombus. In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?