Mathematics - Area of Parallelograms and Triangles
Exam Duration: 45 Mins Total Questions : 30
The area of a rhombus is 60 cm2. lf one of its diagonals is 15 cm, find the other diagonal.
- (a)
4 cm
- (b)
8 cm
- (c)
10 cm
- (d)
16 cm
One of the diagonals of a quadrilateral is 16 cm. The perpendiculars drawn to it from its opposite vertices are 2.6 cm and 1.4 cm. Find its area.
- (a)
32 cm2
- (b)
40 cm2
- (c)
26 cm2
- (d)
28 cm2
The base and corresponding altitude of a parallelogram are 18 cm and 6 cm respectively. What is its area?
- (a)
36 cm2
- (b)
40 cm2
- (c)
44 cm2
- (d)
108 cm2
In ΔABC, AB = 8 cm. If the altitudes corresponding to AB and BCare 4 cm and 5 cm respectively, find the measure of BC.
- (a)
6.4 cm
- (b)
4.6 cm
- (c)
5.4 cm
- (d)
4.5 cm
The diagonals AC and BD of a parallelogram ABCD intersect at O. P is a point on AC such that AP=\(\frac { 1 }{ 4 } \)AC. Which of the following is true?
- (a)
ar(ΔADP) = ar(ΔAPB)
- (b)
ar(ΔADP)=ar(ΔDOC)
- (c)
ar(ΔADP)=ar(ΔBCD)
- (d)
ar(ΔADP)=ar(ADB)
If E, F, G and H are respectively the mid points of the sides of a parallelogram ABCD and ar (EFGH) = 40 cm2, find the ar (parallelogram ABCD).
- (a)
40 cm2
- (b)
20 cm2
- (c)
80 cm2
- (d)
60 cm2
If a triangle and a square are on the same base and between the same parallels, What is the ratio of their areas in order?
- (a)
1:3
- (b)
1:2
- (c)
3:1
- (d)
1:4
Observe the figures given and choose the incorrect statements.
- (a)
ar(ΔAPB) = ar(ΔQCD)
- (b)
ar(ABQD) = 2ar(APQD)
- (c)
ar(ABQD) = ar(ΔABP) + ar(APQD)
- (d)
ar(ADCP) = ar(ΔABP) + ar(APQD)
Observe the figures given and choose the incorrect statements.
- (a)
ar(ΔBCE)=\(\frac { 1 }{ 2 } \)ar(ABCD)
- (b)
ar(ΔBCE) = 2ar(ABCD)
- (c)
ar(ΔBCE) = ar(ABCD) - ar(ΔEDC) - ar(ΔEBA)
- (d)
ar(ΔBCE) = ar(ABCD) - [ar(ΔEDC) + ar(ΔEBA)]
In the given figure. AB II DC. Identify the triangles that have equal areas.
- (a)
ΔADX, ΔACX
- (b)
ΔADX, ΔXCB
- (c)
ΔACX, ΔXDB
- (d)
All the above
In the given figure, if p //q. what is the area of ΔABC?
- (a)
77 cm2
- (b)
38.5 cm2
- (c)
40 cm
- (d)
19.25 cm2
AD is the median of a ΔABC and the area of ΔADC = 15 cm2. Find the ar (ΔABC).
- (a)
15 cm2
- (b)
22.5 cm2
- (c)
30 cm2
- (d)
37.5 cm2
A triangle and a rhombus are on the same base and between the same parallels. What is the ratio of area of triangle to that of rhombus?
- (a)
1:1
- (b)
1:2
- (c)
1:3
- (d)
1:4
Pis a point in the interior of parallelogram ABCD
If ar (IIgm ABCD) = 18 cm2. what is the value of [ar (ΔAPD) + ar (ΔCPB)]?
- (a)
9 cm2
- (b)
12 cm2
- (c)
18 cm2
- (d)
15 cm2
In the given figure, D is the mid-point of BCand L is the mid-point of AD. If ar (ΔABL) = x ar (ΔABC),what is the value of x?
- (a)
2
- (b)
\(\frac { 1 }{ 2 } \)
- (c)
\(\frac { 1 }{ 4 } \).
- (d)
4
In the given figure, what is the area of parallelogram ABCD?
- (a)
AB x BM
- (b)
BC x BN
- (c)
DC x DL
- (d)
AD x DL
In ΔABC, AB = 16 cm, BC = 9.6 cm, CD丄AB. lf CD = 6 cm, find AE.
- (a)
10 cm
- (b)
48 cm
- (c)
8.4 cm
- (d)
9.6 cm
In the figure ABCD is a rectangle inscribed in a quadrant of a circle of radius 10 em. If AD = 2\(\sqrt{5}\) cm, find the area of the rectangle.
- (a)
30 cm2
- (b)
50 cm2
- (c)
40 cm2
- (d)
35 cm2
In the given figure, D, E and F are the mid-points of the sides BC, CA and AB respectively. If ar (BDEF) = x ar (ΔAFE), what is the value of x?
- (a)
\(\frac{1}{2}\)
- (b)
1
- (c)
2
- (d)
4
ABCD is a parallelogram and P is the midpoint of AB. lf ar(APCD) = 36 cm2. find ar(ΔABC)
- (a)
36 cm2
- (b)
48 cm2
- (c)
24 cm2
- (d)
42 cm2
In the given figure, ABCD is a parallelogram AE \(\bot \) DC and CF \(\bot \) AD. If AD = 12 cm, AE = 8 cm and CF = 10 cm, then find CD.
- (a)
17 cm
- (b)
12 cm
- (c)
10 cm
- (d)
15 cm
The median of the triangle divides it into two
- (a)
Triangles of equal area
- (b)
Congruent triangles
- (c)
Right angled triangles
- (d)
Isosceles triangle
In the given figure, ABCD is a parallelogram and Pis mid-point of AB. If ar(APCD) = 36 crn2, then ar (\(\Delta\)ABC) =
- (a)
36 cm2
- (b)
48 cm2
- (c)
24 cm2
- (d)
None of these
In the given figure, if ABCD is a parallelogra and E is the mid-point of BC, then ar(\(\Delta\)DEC = k ar(ABCD). Find k
- (a)
2
- (b)
\(\frac { 1 }{ 4 } \)
- (c)
\(\frac { 1 }{ 2 } \)
- (d)
\(\frac { 2 }{ 3 } \)
ABC is a triangle in which D is the mid-point of BC and E is the mid-point of AD such that the area of \(\Delta\)BED = K area of \(\Delta\)ABC. Find K.
- (a)
2
- (b)
\(\frac { 1 }{ 4 } \)
- (c)
4
- (d)
\(\frac { 1 }{ 2 } \)
In the given figure, if ar (\(\Delta\)ABC) = 28 cm then ar (AEDF) =
- (a)
21 cm2
- (b)
18 cm2
- (c)
16 cm2
- (d)
14 cm2
ABCD is a rectangle with O as any point in its interior. If ar (\(\Delta\)AOD) = 3 crn2 and ar (\(\Delta\)BOC) = 6 cm 2, then area of rectangle ABCD is
- (a)
9 cm2
- (b)
12 cm2
- (c)
15 cm2
- (d)
18 cm2
If E, F, G and H are the mid-points of sides of a parallelogram ABCD then ar(EFGH) = ________
- (a)
\(\frac { 1 }{ 3 } \)ar(ABCD)
- (b)
ar(ABCD)
- (c)
\(\frac { 1 }{ 2 } \)ar(ABCD)
- (d)
\(\frac { 1 }{ 4 } \)ar(ABCD)
Read the statements carefully and write 'T' for true and 'F' for false.
(a) Two parallelograms on the same base and between the same parallel lines are of unequal areas.
(b) The ratio of area of rectangle and a triangle having the same base and between the same parallel is 2 : 1.
(c) The area of a parallelogram is the product of its base and the corresponding altitude.
- (a)
(a) (b) (c) F T F - (b)
(a) (b) (c) T T T - (c)
(a) (b) (c) T F T - (d)
(a) (b) (c) F T T
ABCD is a parallelogram. X and Y are the mid-points of BC and CD respectively. Then, ar (\(\Delta\)AXY) =
- (a)
ar (\(\Delta\)DBC)
- (b)
\(\frac { 3 }{ 8 } ar({ || }^{ gm }ABCD)\)
- (c)
\(\frac { 1 }{ 2 } ar({ || }^{ gm }ABCD)\)
- (d)
ar (\(\Delta\)CYX)
