# 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. Goniometric form Determine goniometric form of a complex number ?.
2. Trapezoid ABCD v2 Trapezoid ABCD has length of bases in ratio 3:10. The area of riangle ACD is 825 dm2. What is the area of trapezoid ABCD?
3. Diamond Determine the side of diamond if its content is S = 353 cm2 and one diagonal u2 = 45 cm.
4. Angles The triangle is one outer angle 158°54' and one internal angle 148°. Calculate the other internal angles of a triangle.
5. Circles 2 Calculate the area bounded by the circumscribed and inscribed circle in triangle with sides 12 cm, 14 cm, 18 cm.
6. Complete construction Construct triangle ABC if hypotenuse c = 7 cm and angle ABC = 30 degrees. / Use Thales' theorem - circle /. Measure and write down the length of legs.
7. Unit vector 2D Determine coordinates of unit vector to vector AB if A[-6; 8], B[-18; 10].
8. Triangle Calculate the sides of the triangle if its area S = 630 and the second cathethus is shorter by 17.
9. Diameter If the endpoints of a diameter of a circle are A(10, -1) and B (3, 10), what is the radius of the circle?
10. Angles ratio In a triangle ABC true relationship c is less than b and b is less than a. Internal angles of the triangle are in the ratio 5:4:9. The size of the internal angle beta is:
11. Isosceles triangle What are the angles of an isosceles triangle ABC if its base is long a=5 m and has an arm b=4 m.
12. RT 11 Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
13. Combi-triangle On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
14. Diamond ABCD In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond.
15. IS trapezoid Isosceles trapezoid arm measured 35 cm. Height is 30 cm and middle segment is 65 cm. Determine length of its bases.
16. Estate Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
17. Angles in triangle The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
18. 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.
19. Diagonals Calculate the length of the diagonals of the rhombus if its side is long 5 and one of its internal angle is 80°.
20. Trapezoid - hard example Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.

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