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## Geometry and Mensuration: Level 1 Test 10

Congratulations - you have completed Geometry and Mensuration: Level 1 Test 10. You scored %%SCORE%% out of %%TOTAL%%. You correct answer percentage: %%PERCENTAGE%% . Your performance has been rated as %%RATING%%
 Question 1
The length and breadth of a playground are 36 m and 21 m respectively. Poles are required to be fixed all along the boundary at a distance 3 m apart. The number of poles required will be
 A 39 B 38 C 37 D 40
Question 1 Explanation:
$\displaystyle \begin{array}{l}The\text{ }total\text{ }number\text{ }of\text{ }the\text{ }poles\text{ }=\\\frac{36}{3}+1+\frac{21}{3}+1+\frac{21}{3}-1+\frac{36}{3}-1\\=\,12+1+7+1+7+12-1-1=38\end{array}$
 Question 2
. The perimeters of a square and a regular hexagon are equal. The ratio of the area of the hexagon to the area of the square is
 A 2âˆš3: 3 B âˆš3: 1 C 3âˆš3: 2 D âˆš2 : 3
Question 2 Explanation:
Let the perimeter be 24 cm.
Thus the area of the square = (24/4)2 =36 cm2
The side of the hexagon = 24/6 cm=4 cm.
There are 6 equilateral triangles in the hexagon.
Each equilateral triangle = (âˆš3/4)x42 =4âˆš3 cm2
Thus the total area of hexagon = 24âˆš3 cm2 =24âˆš3
The required ratio =24âˆš3 : 36 = 2âˆš3 : 3
 Question 3
A rectangular piece of cardboard 18 cm x 24 cm is made into an open box by cutting a square of 5 cm side from each corner and build up the side. Find the volume of the box.
 A 432 cu cm B 560 cu cm C 216 cu cm D None of these
Question 3 Explanation:
The volume of the box is
(18-2x5)(24-2x5)(5) = 560 cu m.
Correct option is (b)
 Question 4
The locus of a point equidistant from the two fixed points is
 A Any straight line bisecting the segment joining the fixed points B Any straight line perpendicular to the segment joining the fixed points C The straight line which is perpendicular bisector of the segments joining the fixed points D Any straight line perpendicular to the line joining the fixed points
Question 4 Explanation:
Imagine a long rubber string (like a guitar string) with a metal ball attached in the middle.
Pull the ball and the pendulum action will be taking place in a straight line.
 Question 5
Any cyclic parallelogram having unequal adjacent sides is necessarily a
 A Square B Rectangle C Rhombus D Trapezium
Question 5 Explanation:
A cyclic quadrilateral has the sum of diagonally opposite angles = 180o
The diagonally opposite angles in a parallelogram are equal.
Thus the angles of the cyclic parallelogram = 90o
The cyclic parallelogram is necessarily a rectangle.
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