Download App

Perimeter and Area — MATHS STD 7 — Question

Gujarat BoardEnglish MediumSTD 7MATHSPerimeter and Area5 Marks
Question
Two cross roads, each of width $5 \ m$, run at right angles through the centre of a rectangular park of length $70 \ m$ and breadth $45 \ m$ and parallel to its sides. Find the area of the roads. Also find the cost of constructing the roads at the rate of ₹ $105 ~per ~m^2$.
✓

Answer

Clearly, area of the cross roads is the area of shaded portion,
i.e., the area of the rectangle $PQRS$ and the area of the rectangle $EFGH$.
But while doing this, the area of the square $KLMN$ is taken twice,
which is to be subtracted once to get the required area.
Now, $P Q=5 \mathrm{~m}$ and $P S=45 \mathrm{~m}$
$\mathrm{EH}=5 \mathrm{~m} \text { and } \mathrm{EF}=70 \mathrm{~m}$
$\mathrm{KL}=5 \mathrm{~m} \text { and } \mathrm{KN}=5 \mathrm{~m}$
Therefore, area of the path = Area of the rectangle $PQRS +$ area of the rectangle $EFGH -$ Area of the square $KLMN$
$=\mathrm{PS} \times \mathrm{PQ}+\mathrm{EF} \times \mathrm{EH}-\mathrm{KL} \times \mathrm{KN}$
$=(45 \times 5+70 \times 5-5 \times 5) \mathrm{m}^2$
$=(225+350-25) \mathrm{m}^2=550 \mathrm{~m}^2$
Hence, cost of constructing the path $=₹ 105 \times 550=₹ 57,750$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Perimeter and Area→Perimeter and Area — all question types→MATHS STD 7 question papers→Gujarat Board STD 7 question papers→Gujarat Board question paper generator→

Similar questions

Consider this data collected from a survey of a colony.
Favourite
Sport		CricketBasket BallSwimmingHockeyAthletics
Watching1240470510430250
Participating620320320250105

Choose an appropriate scale and draw a double bar graph. Write down your observations.
→
Your friend found the median and the mode of a given data. Describe and correct your friends error if any $35,32,35,42,38,32,34$.
Median $=42$ and Mode $=32$
→
If $2^{1998}-2^{1997}-2^{1996}+2^{1995}=k \cdot 2^{1995}$, then find the value of $k$.
→
A number consists of two digits whose sum is $8.$ If $18$ is added to the number its digits are reversed. Find the number.
→
One metre wide path is built inside a square park of side $30m$ along its sides. The remaining part of the park is covered by grass. If the total cost of covering by grass is $Rs. 1176$, find the rate per square metre at which the park is covered by the grass.
→
Write five pairs of integers $(a, b)$ such that a $\div b = –3$. One such pair is $(6, –2)$ because $6 \div (–2) = (–3)$
→
Observe the given bar graph carefully and answer the questions that follow.

$a.$ What information does the bar graph depict?
$b.$ How many motor bikes were produced in the first three months?
$c.$ Calculate the increase in production in May over the production in January.
$d.$ In which month the production was minimum and what was it?
$e.$ Calculate the average $($mean$)$ production of bikes in $6$ months.
→
$6(1 - 4x) + 7(2 + 5x) = 53$
→
Find $x, y, z$ (whichever is required) from the figure given below:
→
Construct an equilateral triangle $ABC$ of side $6\ cm.$
→