# 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. Triangle angles The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
2. Sector The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.
3. EQL triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
4. Euklid4 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
5. Geodesist Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ...
6. Parallelogram Calculate the area and perimeter of a parallelogram whose two sides are long a=24 cm b=22 cm and height ha = 6 cm long.
7. Equilateral triangle Calculate the side of an equilateral triangle, if its area is 892 mm2.
8. XY triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
9. Heron backlaw Calculate missing side in a triangle with sides 17 and 34 and area 275.
10. Slope of the pool Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 1.13 m (for children) and depth at end is 1.84 m (for swimmers). Slope express as percentage and as angle in degrees.
11. Wheat The rectangle shaped field with dimensions 1268 m and 745 m harvested last year was 4959 q wheat. (1 q = 1 quintal = 100 kg). During the year, it was necessary to fix the pipe and therefore did kick wide 4 m parallel to the side of the field 745 m, where n
12. Shooter The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
13. Wiring Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 \$mm2?
14. Nine-gon Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
15. Compass What angle are between directions WSW (WestSouthWest) and SSE (SouthSouthEast) on the compass?
16. Side c In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
17. Height difference What height difference overcome if we pass road 1 km long with a pitch21 per mille?
18. Circle From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
19. Black building Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin Average climb of the road is given by ratio 1:15. By what angle road average climb?