QUADRILATERAL PROBLEMS

1. The diagonal of a rectangle is 25 meters long and makes an angle of 36° with one side of the

rectangle. Find the area and the perimeter of the rectangle.

2. A rectangle and a square have the same area. If the length of the side of the square is 6 units

and the longest side of the rectangle is 5 more than the measure of the shorter side. Find the

dimensions of the rectangle.

3. A certain city block is in the form of a parallelogram. Two of its sides measure 32 𝑓𝑡 and 41 𝑓𝑡.

If the area of the land in the block is 656 𝑓𝑡2, what is the length of its longer diagonal.

4. An isosceles trapezoid has an area of 40𝑚2 and an altitude of 2m. Its two bases have ratio 2 is

to 3. What are the lengths of the bases and one diagonal of the trapezoid?

5. A rhombus has diagonals of 32 and 20 inches. Find the angle opposite the longer diagonal. Also

determine its area.

6. If the diagonal length of a square is tripled, how much is the increase in the perimeter of the

square?

7. The area of the rhombus is 156𝑚2. If its shorter diagonal is 13 m, find the longer diagonal.

8. The official ball diamond is in the form of a square. The distance between the home base and

the second base in a baseball is usually 35m. Find the area and the distances between the

bases.

9. A piece of wire is shaped to enclose an equilateral triangle whose area is 16√3𝑐𝑚2. It is then

reshaped to enclose a rectangle whose length is 9 cm. Find the area of the rectangle.

10. A rectangle 𝐴𝐵𝐶𝐷, which measures 9ft by 12ft, is folded once perpendicular to diagonal AC

so that the opposite vertices A and C coincide. Find the length of the fold.

Answers:

1. 297𝑚2, 69.84𝑚

2. 9 𝑏𝑦 4

3. 70.55 ft

4. 16m, 24m, 20.1m

5. 116°, 320𝑖𝑛2

6. 3 𝑡𝑖𝑚𝑒𝑠 7. 24m

8. 612.5𝑚2, 24.75𝑚

9. 27𝑐𝑚2

10. 11.25 𝑓𝑡