CAPSTONE
Mathematics: Geometry ~q
Lecture 10
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* Basic Geometry: ¢ Advance Geometry:
1. Angle 1. Circle
2. Triangle 2. Solid Geometry
3. Quadrilateral
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Qwwwcapstonebd.com — Capstone Education Math Lecture Sheet: 10
Some Common Terms:
Triangle Circle
Right triangle Semicircle
Equilateral triangle Are
Isosceles triangle Chord
Scalene triangle Diameter
Similar triangle Radius
Angle Circumference
Central Angi Tangent
Exterior Angle Quadrilateral
Interior Angle Rectangle
Right Angle Square
Obtuse Ang 7 Parallelogram
‘Acute Angle Rhombus
Reflex Angle Altitude
Straight Angle Base
Complementary Angle worm Perpendicular
Supplementary Angle Ee Hypotenuse
Adjacent Angle fife ca Vertex
Vertical Angle edn corr Median
Alternate Angle Area
Corresponding Angle Perimeter
Cube Congruent
Inscribed Volume
Diagonal Parallel area
Bisector oiferse
Aagle: Two line or line-segments are required to form an angle. An angle is represented by Zsign.
Right angle: Right angle is 90° angle. When two lines are perpendicular, a right angle is formed and it is
expressed with sign, Below is a right angle. Obtuse angles: Angles greater than 90° but smaller than 180°.
Acute angles: Angles greater than 0° but less than 90°,
Straight angle: An angle whose degree measure is exactly 180°.
ee
Acute Obtuse Straight
[x<90)] 90°
AB+BC
E, None of these
1. ABCD is rectangle. 22XD = 30° and 2AZY = 80°. Find 2ZYB. [BBA 14-15]
A y B
x
A. 100° B. 110° C. 120° . E. None of these
12. A towel, when balanced was found to have lost 20% of its length and 10% of its breadth. The percentage
of decreases in area is -
A. 10% B, 10.08% €. 20% D. 28% E. 30%
13, In the figure, AD is parallel to BC. BC = 12 cm and AD = 3 em, If AE = 2 cm what is the length of EC
in cm? [BBA 14-15]
A.6 B.S D.12 E. None of these
'4. The diagonal of a rectangle is V#I em and its area is 20 cm*. What is the perimeter of the rectangl
A.l6em B. 17cm C.20.cm D. 18cm E. None of these 15. The rhombus ABCD has diagonals intersecting at X, with BC = 13 em and CX = 5 em. Calculate the
area of the rhombus in em’,
A. 65 B.90 c. 120 D.130 E. None of these
16. The length of a rectangular field X is 2 kilometers greater than the side of a square field Y and the width
of the field X is 2 kilometer less than the side of filed Y. If Y" is the area of Y in square kilometer, which of
the following gives the area, in square kilometers, of field X?
AY? =4 B.y?-2 y2 Dy? +2 E, None of these
17. In the figure, 2CAB = 2banda>e
D.b>aandb E. None of these
3. What is the perimeter of the shaded region in the following square whose length of the side is 2 and M
and N are the middle points of the two sides?
Mi
A3 B.2+3V2 C.3 + 2v2 D.S E. None of these
4. If the hypotenuse of an isosceles right triangle has length of 8, then the area of the triangle is -
Ad B.4v2 C8 D.16 E. None of these
5. The longest side of an isosceles right triangle measure 16 m. What is the perimeter of the triangle?
A, 32V2 m B, 32 + 16y2 C.16 + 16v2 D. 32 + v2m E. None of these
6. Ifthe length of a side of an equilateral triangle is 4 om. Its height is -
A. 2v3 B.4v3 C. 16v3 D.33V2 E, None of these
7. In the figure below, triangle ABC is isosceles with base AC. If x = 60°, than AC
B
A2 B.3
8. What is the value of *x’ in the figure below?
E. None of these 9. The area of a triangle with sides 3 em, 5 em and 6 em is -
A. 2y3em? B. 2yT4em* C. SVT2cm? D. 4V%cm? E. None of these
10. If the length of rectangle A is one-half the length of rectangle B, and the width of rectangle A is one-half
the width of rectangle B, what is the ratio of the area of rectangle A to the area of rectangle B?
At B.S cal D2 BE
11. The length of one edge of a square equals 4. What is the distance between the center of the square and
one of its vertices?
A2 B. 2v2 C.2v3 D.4v2 E. None of these
12. The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting
rectangle exceeds the area of the square by -
A.30 B.76 C82 D.4l E, None of these
13. IP the length of each of the sides of three square garden’s plots is increased by 50 percent, by what
percent is the sum of the areas of the three plots increased?
A. 125% B. 150% €. 200% D. 375% E. None of these
14. A square carpet with an area of 169 cm? must have 2 cm cut off one of its edge in order to be a perfect fit
for a rectangle room. What is the area (in cm?) of this rectangular room?
ALLIT B. 143 Cc. 145, D. 165 E. None of these
15. The area of a rectangle R with width 4 fi is equal to the area of a square S, which has a perimeter of 24
fi. The perimeter of the rectangle R, in feet is -
Ao B.16 C.24 D.26 E.30
16. The length of a rectangle is three times its breadth. What is the perimeter of the rectangle (in meter) if its
length is 48 meters?
A.30 B. 60 C.96 D.128 E. None of these
17. The ratio between the perimeter and the breadth of rectangle is 5:1. If the area of rectangle is 216 sq.
em, what is the length of the rectangle?
A. 16m B.24cm C.200m D. 18 cm E. 1S em
|S. A reciangular rug covers half of a rectangular floor that is 9 feet wide and 12 feet long, Ifthe dimensions
of the rug are in the same ratio as those of the floor, how many feet long is the rug?
AG B.8 C.10 D.12
E. None of these 19. The area of a rectangular plot is 460 square meters. If the length is 15% more than the breadth, what is
the breadth of the plot?
Ala B.20 C24 D.28 E. None of these
20. If the area of a rhombus is 54 sq. cm and the length of one of the diagonals is 6 em then the length of the
other diagonal is -
AL18 B.12 co D.6 E. None of these
21. In the figure, ABCD is a rectangle and AF is parallel to BE. If BC = CE = 5 cm and AB = 10 cm, then
what is the area of AAFD in em??
E
C.25 D.50 E. None of these
22. If the area of a rectangular is equal to the area of @ square, then the perimeter of the rectangular must be -
A. Half the perimeter of the square B. Equal to the perimeter of the square
C. Equal to twice the perimeter of the square. Equal to the square of the perimeter of the square
E, None of these
23, In the figure below, PQRS is a square and M and N are midpoints of their respective sides, Each side of
the square has a length of 4 inches. What is the area of quadrilateral PMRN?
P M Q
A.8 sq. inches B, 10sq. inches. 12 sq. inches . E, None of these
24. One of the sides of a square measures 20 cm in length. If we increase the length of two opposite sides by
4 centimeters and decreases f i ite si
timeters and decreases the length of the remaining two opposite sides by the same measure, then what
be the area of the resulting figure in sq. em?
as ia [MBA 2013]
D. 400 E. None of these 25. In the figure, if CP = BP and X = 120°, then y
A. 30 B.45 E. None of these
26. In the figure AB = AC = 4 em and ZBAC = 120°. Find the area of the triangle.
A
A. 8yT2 B. 4VT2, ©. 2vT2 D.16 E. None of these
27. The figure below is an equilateral triangle divided into four congruent small, equilateral triangle. If the
perimeter of a smaller triangle is 1, what is the perimeter of the larger triangle?
C6 D.8
B.4
28. In the figure, what is the value of y? [July 2016]
4x2
DEL
A.20 B.25 C30 D.35 E. None of these
E. None of these 30. In the parallelogram, E is the midpoint of AC and EF is parallel to AB, If the area of ABCD is 36 sq.cm
and EX = 6 cm, what is the area of triangle ABX in sq.cm? A B
A.16 B.15
D9 E. None of these