MENSURATION 2D TEST

1. Find the area of triangle whose sides are 10 cm, 12 (a) 250 m2 (b) 400 m2
cm, and 18 cm. (c) 200 m 2
(d) 300 m2
10 lseh, 12 lseh vkSj18 lseh Hk
qtkvksa okys f=kHkqt dk
{ks=kiQy
8. The side of an equilateral triangle is 28 cm. Taking
Kkr dhft,A each vertex as the centre, a circle is described with a
2 2
radius equal to half the length of the side of the
(a) 22 2 cm (b) 30 2 cm
triangle. Find the area of that part of the triangle
(c) 28 2 cm2 (d) 40 2 cm2 22
2. The perimeter of an isosceles right-angled triangle which is not included in the circles (use  = and
7
2
having an area of 200 cm is: 3 = 1.73).
fdlh lef}ckgq ledks.k f=kHkqt dk ifjeki D;k gksxk] ftldk {ks=kiQy
200 lseh2 gSA ,d le ckgq f=kHkqt dh Hkqtk 28 lseh gSA çR;sd 'kh"kZ dks osaQ
(a) 68.3 cm (b) 78.2 cm f=kHkqt dh Hkqtk dh vkèkh yackbZ osQ cjkcj f=kT;k okys ,d o`Ù
(c) 70.6 cm (d) 58.6 cm fpf=kr fd;k x;k gSA f=kHkqt osQ ml Hkkx dk {ks=kiQy Kkr dh
3. Two circles of radius 7 units each, intersect in such 22
a way that the common chord is of length 7 units.  =gS ( vkSj 3 = 1.73 dk mi;ksx
tks o`Ùk esa 'kkfey ugha
7
What is the common area in square units of the dhft,)A
intersection?
(a) 30.89 cm² (b) 38.08 cm²

A
çR;sd 7 bdkbZ f=kT;k okys nks o`Ùk bl çdkj çfrPNsn djrs gSa fd
(c) 31.08 cm² (d) 39.08 cm²
mHk;fu"B thok dh yackbZ 7 bdkbZ gksA çfrPNsnu dk oxZ9. bdkb;ksa esa
A rectangular lawn whose length is twice of its breadth
mHk;fu"B {ks=kiQy D;k gksxk\ is extended by having four semi-circular portions on
 3  3 its sides. What is the total area (in m2) of the lawn if the

Y
(a) 98  –  (b) 98  –  smaller side of the rectangle is 12 m? (Take  = 3.14)
6 3  3 4 
,d vk;rkdkj ykWu] ftldh yackbZ mldh pkSM+kbZ dh rqyuk eas nksx
 3  3
(c) 98  –  (d) 98  –  Hkqtkvksa ij pkj v/Zo`Ùkkdkj Hkkxksa osQ lkFk c<+k;k tkrk gSA ;fn
6 6  6 4 
4. Find the area (in cm²) of the sector whose perimeter
12 ehVj gS] rks ykWu dk oqQy {ks=kiQy
NksVh Hkqtk ² esa)(ehVj
Kkr djsaA

is
64
3
H
cm and central angle is 60°. (Use  =
22
7
)
(a) 548.32
(c) 853.2
(b) 444
(d) 308.64
10. The ratio of the length of each equal side and the third
ml f=kT;•aM dk {ks=kiQy2 (lseh
esa) Kkr dhft, ftldh ifjf/ side of an isosceles triangle is 3:5. If the area of the
triangle is 30 11 cm² then the length of the third side
S
64
lseh vkSj osaQæh; dks.k
60° gSA( = 22/7 dk mi;ksx dhft,A
3 (in cm) is:
47 77 ,d lef}ckgq f=kHkqt dh izR;sd leku Hkqtk dh yackbZ vkSj rhl
(a) (b)
3 3 Hkqtk dh yackbZ dk vuqikr
3 : 5 gSAfn; f=kHkqt dk {ks=kiQy
K

(c)
68
(d)
85 30 11 lseh2 gS] rks rhljh Hkqtk dh yackbZ (lseh esa) D;k gksxh\
3 3
5. The perimeter of a parallelogram is 48 cm. If the (a) 10 6 (b) 5 6
height of the parallelogram is 6 cm and the length of (c) 13 6 (d) 11 6
the adjacent side is 8 cm. find its area.
LA

11. The area of a triangular park with sides 88 m, 165 m,

,d lekarj prqHkZqt dk ifjeki 48 lseh gSA ;fn lekarj prqHkZqt dh ÅapkbZ
and 187 m is equal to the area of a rectangular plot whose
6 lseh gS vkSj vklUu Hkqtk dh yackbZ 8 lseh gSA bldk {ks=kiQy Kkr dhft,\
sides are in the ratio 5 : 3. What is the perimeter (in m)
(a) 90 cm 2
(b) 80 cm 2 of the plot?
(c) 84 cm2 (d) 96 cm2 88 e hVj]165 e hVj vkSj187 e hVj Hkqtkvksa okys ,d f=kdks.kh;
ikoZQ dk {ks=kiQy ,d vk;rkdkj Hkw•aM osQ {ks=kiQy osQ c
6.
 16 
The perimeter of equilateral triangle is 3 ×  4  5 : 3 g SA Hkw•aM dk ifjeki (ehVj esa)
ftldh Hkqtkvksa dk vuqikr
 3  D;k gS\
units. Determine the area of the triangle. (a) 352 (b) 384
(c) 400 (d) 320
 16 
leckgqf=kHkqt dk ifjeki
3 ×  4  bdkbZ A
gSf=kHkqt dk {ks=kiQy
12. What is the difference in area (in cm²) of ABC having
 3  sides of 10 cm, 20 cm and 20 cm, and a right angled
Kkr dhft,A  PQR with hypotenuse of 13 cm and one of the
(a) 4 unit² (b) 1 unit² perpendiculars of 12 cm?
(c) 3 unit² (d) 2 unit² 10 lseh, 20 lseh vkSj20 lseh Hkqtkvksa okys ABC rFkk 13
7. What will be the area of a plot of quadrilateral shape, lseh d.kZ vkSj yacksa 12
esalseh
ls osQ ,d yac okys ledks.k f=kHkqt
one of whose diagonals is 20 m and lengths of the PQR osQ {ks=kiQy cm²( e sa) esa fdruk varj gksxk\
perpendiculars from the opposite vertices on it are
Note: 2 = 1.41, 3 = 1.73, 7 = 2.65, 13 = 3.61, 15 =
12 m and 18 m, respectively?
pr qHkZqt vkdkj osQ ,d Hkw•aM dk {ks=kiQy D;k gksxk] ftlosQ
3.87,,d 21 = 4.58
fod.kZ dh yackbZ 20 ehVj gS vkSj ml ij foijhr 'kh"kks± ls (a) 70.05
Mkys (b) 36.57
(c) 66.75 (d) 53.58
x, yacksa dh yackbZ Øe'k% 12 ehVj vkSj 18 ehVj gS\

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13. A farmer's land is in the shape of a trapezium which osQaæ 22.5°
ij osQ dks.k dks varfjr djus okys ,d o`Ùk osQ f=kT;[kaM
has its parallel sides measuring 6.32 yards and 7.68
dk {ks=kiQy346.5 lseh2 fn;k x;k gSA o`Ùk dh f=kT;k (lseh esa) D;k
yards and the distance between the parallel sides is
5.50 yards. The cost of ploughing the land is Rs 1200 gksxh\(= 22/7 dk iz;ksx djsa
)
per square yard. What amount have to be spent in (a) 35 (b) 45
order to plough the entire land? (c) 42 (d) 48
,d fdlku dh Hkwfe ,d leyac osQ vkdkj dh gS ftldh lekukarj 18. The diagonal of a square A is (a + b) units. What will
Hkqtk,¡ 6-32 xt vkSj 7-68 xt gSa vkSj lekukarj Hkqtkvksa osQbechp the area (in square units) of the square drawn on
dh nwjh 5-50 xt gSA tehu dh tqrkbZ dk •pZ 1200 #i;s çfr the diagonal of square B, whose area is twice the area
oxZ xt gSA iwjh tehu tksrus esa fdruh jkf'k •pZ djuh iM+sxh\ of square A?
(a) `36600 (b) `32500 ,d oxZA dk fod.kZ (a + b) bdkbZ gSA B, ft ldk {ks=kiQy
oxZ
(c) `55400 (d) `46200 oxZA osQ{ks=kiQy ls nksxquk gS] mlosQ fod.kZ ij [khaps x, oxZ
14. The sum of the radii of two circles is 286cm and the {ks=kiQy (oxZ bdkbZ esa) fdruk gksxk\
area between the concentric circles is 50336 cm².
What are the radii (in cm) of the two circles? [Take (a) (a + b)2 (b) 2(a + b)2
2
 = 22/7] (c) 4(a + b) (d) 8(a + b)2
nks o`Ùk dh f=kT;kvksa dk 286;ksx
lsehgS vkSj laosaQfær o`Ùkksa osQsides of a triangle are 24 cm, 26 cm and 10 cm,
19. The
50336 l seh
eè; dk {ks=kiQy ² g SA nksuksa o`Ùkksa dh f=kT;k,aAt each of its vertices, circles of 2radius 4.2 cm are
( lseh
drawn. What is the area (in cm ) of the triangle,
22 excluding the portion covered by the sectors of the
esa
) fdruh&fdruh gksaxh\ eku ysa)A

A
(= circles?
7
[Take  = 22/7]
(a) 91 and 84 (b) 171 and 84
fdlh f=kHkqt dh Hkqtk,a
24 l seh
, 26 l seh vkSj10 lseh gS
A blosQ
(c) 115 and 91 (d) 115 and 171
ij lsehf=kT;k okyk o`Ùk [khapk tkrk gSA o`Ùkks
izR;sd 'kh"kZ4.2
15. Half the perimeter of a rectangular garden, whose

Y
length is 8 cm more than its width, is 42 cm. Find [kaMksa }kjk doj fd, x, Hkkx dks NksM+dj] f=kHkqt dk {ks
the area of the rectangular garden. (lseh² esa) Kkr djsaA
,d vk;rkdkj cxhps dk vk/k ifjeki 42 lseh gS] ftldh yackbZ (a) 27.72 (b) 120
mldh pkSM+kbZ ls 8 lseh vf/d gSA vk;rkdkj cxhps dk {ks=kiQy (c) 105.86 (d) 92.28
Kkr dhft,A
(a) 542 cm2 (b) 425 cm2
H 20. If the sum of the diagonals of a rhombus is L and
the perimeter is 4P, then find the area of the
2
rhombus?
(c) 254 cm (d) 524 cm2
16. The area of the rhombus (in cm²) having each side equal ;fn ,d leprqHkZqt osQ fod.kks± dk L;ksx
vkSj mldk ifjeki
4P gS] rks ml leprqHkZqt dk {ks=kiQy D;k gksxk\
S
to 13 cm and one of its diagonals equal to 24 cm is:
ml leprqHkqZt dk {ks=kiQy² (lseh
esa) D;k gS] ftldh izR;sd Hkqtk 1 2
13 lseh gS vkSj ,d fod.kZ 24 lseh gS\
(a)
4
 L – P2 
(a) 120 (b) 60 1 2
(b)  L – 4P 2 
K

(c) 110 (d) 130 4

17. The area of a sector of a circle that subtends a 22.5° 1 2
angle at the center is given as 346.5 cm2. What will be (c)
2
 L – 4P 2 
the radius (in cm) of the circle? 1 2
[Use  = 22/7] (d)
4
 L  3P 2 
LA

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