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MATHS [3 marks sum]

Mensuration · ICSE STD 7 (ICSE - English Medium). 18 questions.

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[3 marks sum]

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18 questions · timed · auto-graded

Question 13 Marks
Find the area of the shaded region in the adjoining figure, it being given that ABCD is a square of side $12 cm, CE =4 cm, FA =5 cm$ and $BG =5 cm$.
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Answer
$68.5 cm^2$
[Hint: Required area $=$ Area of square $-[$ area of $\triangle A F G+$ area of $\triangle B G C+$ area of $\triangle D E F]$
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Question 23 Marks
Find the area of the shaded region of the adjoining figure, it being given that $\angle FAB =\angle CBA =90^{\circ}, ED \| AB \| FC , EG \perp FC , DH \perp FC$, $FG = HC , AB =15 cm, AF =9 cm, ED =8 cm$ and distance between AB and $ED =13 cm$.
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Answer
$181 cm^2$
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Question 43 Marks
Find the area of the quadrilateral ABCD , given in the adjoining figure in which $AB =14 cm, BC =78 cm$, $CD =112 cm, BD =50 cm$ and $DA =48 cm$.
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Answer
$2016 cm^2$
[Hint : Area of quadrilateral ABCD $=$ Area of $\triangle A B D+$ Area of $\triangle D B C$.]
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Question 53 Marks
Find the area of a quadrilateral ABCD whose diagonal AC is 25 cm long and the lengths of perpendiculars from opposite vertices B and D on AC are $BE =3.6 cm$ and $DF =2.4 cm$.
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Answer
$75 cm^2$
[Hint: Area of quadrilateral ABCD$=($ area of $\triangle A B C)+($ area of $\triangle A C D)$$\left.=\left(\frac{1}{2} \times A C \times B E\right)+\left(\frac{1}{2} \times A C \times D F\right)\right]$
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Question 63 Marks
Calculate the area of the quadrilateral PQRS shown in the adjoining figure, it being given that $PR =8 cm, RQ =17 cm, \angle RPQ =90^{\circ}, RS =6 cm$ and $\angle PRS =90^{\circ}$.
Image
Answer
$105 cm^2$
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Question 73 Marks
Calculate the area of the quadrilateral ABCD in which $AB = BD = AD =10 cm, \angle BCD =90^{\circ}$ and $CD =8 cm$. (Take $\sqrt{3}=1.732$ ).
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Answer
$67.25 cm^2)
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Question 83 Marks
The central hall of a school is 22 m long and 15.5 m wide. A carpet is to be laid on the floor leaving a strip of 75 cm width from the walls uncovered. Find the area of the carpet and the area of the strip left uncovered.
Answer
$287 m^2, 54 m^2$
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Question 93 Marks
A rectangular lawn 115 m long and 64 m broad has two cross-paths at right-angles, one 2 m wide, running parallel to its length and the other 2.5 m wide, running parallel to its breadth. Find the cost of gravelling the paths at ₹ 114 per $m ^2$.
Answer
43890
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Question 103 Marks
A path 2.5 m wide is running around a rectangular grassy plot 40 m by 35 m . Find the area of the path and the money needed for tilling it at $₹ 115.60$ per $m ^2$.
Answer
$400 m^2$, ₹ 46240
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Question 113 Marks
A path 3 m wide is running along the inside of the boundary of a rectangular field 116 m by 76 m . How much money is needed to gravel the path at $₹ 42.50$ per $m ^2$ ?
Answer
47430
[Hint: Area of path $=116 \times 76-110 \times 70=1116 m^2$
$\therefore$ Total cost $=₹ 1116 \times 42.50=₹ 47430$.
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Question 123 Marks
A sheet of paper measures 35 cm by 25 cm . A strip of 5 cm width is cut from it, all around. Find the area of the remaining sheet and also the area of the cut-out strip.
Answer
$375 cm^2, 500 cm^2$
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Question 133 Marks
A hall is 16 m long and 12 m broad. Find the cost of carpeting it at $₹ 615$ per $m ^2$, after leaving a margin of 1 metre all around.
Answer
86100
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Question 143 Marks
A room is 10 m long and 6 m broad. It is surrounded by a verandah which is 2 m wide all around it. Find the cost of flooring the verandah with marble at $₹ 236$ per $m ^2$.
Answer
18880
[Hint: Area of floor of verandah $=14 \times 10-10 \times 6=80 m^2$
The cost of flooring the verandah $=₹ 236 \times 80$ ]
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[3 marks sum] - MATHS STD 7 Questions - Vidyadip