Download Worksheet 5

Worksheet 5
1. Three sides of a symmetrical trapezoid are of length 10, the fourth side has length 20.
Calculate the angles and the area of the trapezoid.
2. The lengths of the two diagonals of a rhombus are given: 6 and 12.
a) Calculate the area of the rhombus!
b) Calculate the length of the sides of the rhombus!
c) Calculate the angles of the rhombus!
3. The sides of rectangle ABCD are AB = 10 and BC = 6. What is the distance of point P on
side AB from vertex D if AP + PC = 12?
4. In a symmetrical trapezium the inclination angle of the diagonal to the longer parallel base
is 45, the length of the diagonal is 10. What is the area of the trapezium?
5. Calculate the lengths of the legs of a symmetrical trapezium if the lengths of the parallel
sides are 9.6 cm and 7.2 cm and the length of the diagonal is 9.2 cm.
6. The bases of a right angled trapezium are 4 cm and 6 cm. One of the angles is 60. What
are the lengths of the legs, the diagonals, and what is the area of the trapezium?
7. The perimeter of a rhombus is 40, its area is 96. What are the angles, sides, and diagonals
of the rhombus?
8. The area of a rhombus is 1 unit. What are the diagonals and the side of the rhombus if one
of the angles is 150?
9. The shortest diagonal of a parallelogram has length 8, the angle of the diagonals is 45,
and its area is 40. Calculate the perimeter of the parallelogram.
10. A deltoid has diagonals 16 and 8 cm long. The 16 cm diagonal is on the symmetry axis of
the deltoid and the other diagonal intersects it at a distance 5 cm from one end. Calculate
the perimeter and the area of the deltoid.
11. In kite ABCD, we know that AB = BC = 2, CD = DA. At vertex A the angle is 120, and
at D the angle is 60. Calculate the unknown angles, lengths sides and diagonals of the
kite, and furthermore, the radius of the inscribed circle.
12. The length of the side of a rhombus is just the geometric mean of the diagonals. What is
the ratio of the two diagonals?
13. The length of the shortest diagonal of a regular octagon is given: 10. What is the length of
the sides, and what is the area of the polygon?
14. The length of the mid-line of a symmetrical trapezium is 10; the diagonals are
perpendicular to each other. What is the area of the trapezium?
15. Draw a rhombus around a circle of area 100, so that the rhombus has an angle 30.
Calculate the area of the rhombus.
16. The acute angles of a symmetrical trapezium are 60, its legs are 12 cm long and the
perimeter is 70 cm. Calculate the lengths of the sides and the area.
17. Find the area of a trapezium if the bases are 5 cm and 13 cm, and the other sides are 7 cm
and 11 cm.
18. The diagonals of a trapezium are perpendicular. The lengths of the parallel sides are 17
and 34, one of the legs is√964. How long is the second leg, what is the area, and the
height of the trapezium?
19. Determine the perimeter and the area of a regular pentagon inscribed in circle with radius
28 cm.
20. The lengths of the two parallel sides of a trapezium are 4 and 2 units. The angle between
the longer diagonal and the parallel sides is 30, and the two diagonals are perpendicular
to each other. What is the length of the shorter diagonal? What are the lengths of the two
segments of the shorter diagonal produced by its intersection with the longer diagonal?
21.