ASSIGNMENT - MENSURATION OF PLANE FIGURES
1. If three lines intersect, then there is exactly one plane that contains them.
2. If two lines intersect, then there is exactly one plane that contains them.
3. A line can be in two different planes
Answer the following problems completely.
1. If the perimeter of a square is 20, what is its area
2. A parallelogram has sides 9 cm and 15 cm lone. If the shorter altitude is 3 cm, what is the length of the longer altitude?
3. If the area of an equilateral triangle is√3, what is the length of each side?
4. The area of a rhombus is 126 square meters, and one of its diagonals measures 14 meters, what is the length of the other diagonal?
5. If an isosceles trapezoid has bases with lengths 12 and 28 and an area of 300, what is its perimeter?
6. Find the area of a regular hexagon with perimeter of 72.
7. If the perimeter of an octagonal stop sign is 80 inches and its height is about 24 inches, what is its area.
8. In a right triangle, the altitude to the hypotenuse separates the hypotenuse into two equal pieces. If the whole hypotenuse is 150, what is the length of the altitude?
9. A rectangle filed has a length of 1200 yards and a diagonal of 1300 yards. What is the width of the field in yards?
10. Two sides of a right triangle are 5 and 15. Which of the following could be the third side?
11. The diagonals of a rhombus measure 16 and 30. What is the perimeter of the rhombus?
12. A commuter drives 8 blocks west and 6 blocks south to get to work. If a block is 50 yards, how many yards would a crow have fly between the two locations?
13. A kite has diagonals measuring 16 and 21. The former divides the latter into pieces of 15 and 6. What is the perimeter of the kite?
14. A pair of corresponding sides of two similar polygons measures 15 and 21. What could be their perimeters?
15. The perimeters of two similar triangles are 54 and 30. The shortest side on the smaller triangle is x, and the corresponding side on the larger triangle is 3x-6. What is the length x?
16. Could 8, 9, 0.1 be the measures of the sides of a triangle?
17. Find the range of the values for the third side of a triangle with sides of length 3 cm
18. A man trapped inside a barrel with a diameter of 36 inches rolls 50 yards down a hill. How many complete revolutions does the man make?
19. If the area of a circle is increased by 21%, by what percent does its circumference increase?
20. If a certain shape is both a rectangle and a rhombus, and one side of it is 3, what is sum of the remaining side measures?
21. Two angles in a parallelogram have a sum of 154. What is the measure of the angle between them?
22. A parallelogram's diagonals have lengths of 24 and 17, and the angle between them measures 90. What is it?
23. If one base of a trapezoid is 10 units long and the midsegment is 13 units long, what is the length of the other base?