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Math Chapter 9 : Topic 3
Polygon Applications
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A square park has side length $20\ m$. If fencing is required around it, the total length of fencing needed is:
Reasoning: Perimeter of square $= 4 \times side = 4 \times 20 = 80\ m$
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A triangular field has base $10\ m$ and height $6\ m$. The area of the field is:
Reasoning: Area $=$ $\frac{1}{2}$ $\times base \times height =$ $\frac{1}{2}$ $\times 10 \times 6 = 30$
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A rectangular carpet is replaced by a parallelogram-shaped carpet having the same base and height. The area will be:
Reasoning: Area of parallelogram $=$ base $\times$ height, same as rectangle
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A regular hexagon has side length $5\ cm$. Its perimeter is:
Reasoning: Perimeter $= 6 \times 5 = 30$
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A triangular garden is doubled in both base and height. Its area becomes:
Reasoning: Area $\propto$ base $\times$ height $\Longrightarrow$ Doubling both $\Longrightarrow$ $2 \times 2 = 4$
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A parallelogram has base $12\ m$ and height $5\ m$. The area is:
Reasoning: Area $=$ base $\times$ height $= 12 \times 5 = 60$
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A floor is tiled with regular square tiles of side $2\ m$. If floor area is $72\ m^{2}$, number of tiles required is:
Reasoning: Tile area $= 4\ \ \ \ \Longrightarrow \ \ \ \ 72 \div 4 = 18$
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The sum of interior angles of a regular pentagon is:
Reasoning: $(n - 2) \times 180^{o} = (5 - 2) \times 180 = 180^{o}$
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Each interior angle of a regular hexagon is:
Reasoning: $540 \div 6 = 120^{o}$
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A parallelogram-shaped wall has base $8\ m$ and height $3\ m$. Cost of painting per $m^{2}$ is constant. Total area to be painted is:
Reasoning: Area $= 8 \times 3 = 24$
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A triangle and parallelogram have same base and height. The triangle's area is:
Reasoning: Triangle area $=$ half of parallelogram
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A regular octagon has $8$ equal sides. If each side is $3\ cm$, its perimeter is:
Reasoning: $8 \times 3 = 24$
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A triangular roof has base $12\ m$ and height $10\ m$. Area of roofing material needed is:
Reasoning: $\frac{1}{2}$ $\times 12 \times 10 = 60$
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If the side of a square tile is tripled, its area becomes:
Reasoning: $Area \propto {side}^{2}\ \ \ \ \Longrightarrow \ \ \ \ 3^{2} = 9$
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A parallelogram has same area as a rectangle of length $10\ m$ and width $4\ m$. Its area is:
Reasoning: Rectangle area $= 10 \times 4 = 40$
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A regular polygon has each interior angle $135^{o}$. Number of sides is:
Reasoning: Exterior angle $= 45\ \ \ \ \Longrightarrow \ \ \ \ 360 \div 45 = 8$
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A triangular plot has sides $3\ m$, $4\ m$, $5\ m$. It is:
Reasoning: $3^{2} + 4^{2} = 5^{2}$[Pythagorean theorem:]$(Perpendicular)^{2}$ $+ (Base)^{2} = (hypotenuse)^{2}$
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If the base of a parallelogram is doubled but height remains same, area becomes:
Reasoning: Area $\propto$ base
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A square garden has area $81\ m^{2}$. Length of one side is:
Reasoning: $= 9$
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A regular polygon has $10$ sides. Number of diagonals is:
Reasoning: $\frac{n(n\ - \ 3)}{2}$ $=$ $\frac{10\ \times \ 7}{2}$ $= 35$
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A parallelogram has area $50\ m^{2}$ and base $10\ m$. Height is:
Reasoning: Height $=$ area $\div$ base $= 50 \div 10 = 5$
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A regular triangle used in tiling has each angle:
Reasoning: Equilateral triangle $\Longrightarrow$ each angle $= 60^{o}$
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If the dimensions of a rectangular carpet are doubled, its area becomes:
Reasoning: Area $\propto$ length $\times$ width $\Longrightarrow$ $2 \times 2 = 4$
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A hexagonal tile has $6$ equal sides. If one side increases, which property remains unchanged?
Reasoning: Number of sides is fixed $(6)$
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A triangular field and rectangular field have same base and height. Which has larger area?
Reasoning: Rectangle area is double triangle
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