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Areas of Triangles and Quadrilaterals — Maths STD 9 — Question

Gujarat BoardEnglish MediumSTD 9MathsAreas of Triangles and Quadrilaterals5 Marks
Question
A rectangular lawn, $75\ m$ by $60\ m$, has two roads, each road 4m wide, running through the middle of the lawn, one parallel to length and the other parallel to breadth, as shown in the figure. Find the cost of gravelling the rosds at ₹ $50$ per $m^2.$​​​​​​​
✓

Answer

For road $A B C D$, i.e. for rectangle $A B C D$,
Length $=75 m$
Breadth $=4 m$
Area of road $A B C D=$ Length $\times$ Breadth $=75 m \times 4 m=300 m^2$
For road PQRS, i.e. for rectangle PQRS,
Length $=60 m$
Breadth $=4 m$
Area of road PQRS $=$ Length $\times$ Breadth $=60 m \times 4 m=240 m^2$
For road EFGH, i.e. for square EFGH,
Side $=4 m$
Area of road EFGH $=(\text { Side })^2=(4)^2=16 m^2$
Total area of road for gravelling
$=$ Area of road ABCD + Area of road PQRS - Area of road EFGH
$=300+240-16$
$=524 m^2$
Cost of gravelling the road $=₹ 50$ per $m ^2$
$\therefore$ Cost of gravelling $524 m^2$ road $=₹(50 \times 524)=₹ 26,200$

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