Tag: problems on areas

Questions Related to problems on areas

The area of a rectangle of length (x + 2) units and breadth (x -8) units is

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $x^2-16$

  2. $x^2-6x-16$

  3. $x^2-10x+16$

  4. $x^2-10$

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Correct Option: B
Explanation:

$l\times b=(x+2)(x-8)$
$=x^2+[(2)+(-8)]x+(2)(-8)$
$=x^2-6x-16$

A closed box made of steel of uniform thickness has length breadth and height 12 dm, 10 sm and 8 dm respectively If the thickness of the steel sheet is 1 dm then the inner surface area is

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $ \displaystyle 456$ $\displaystyle dm^{2}$

  2. $ \displaystyle 376$ $\displaystyle dm^{2}$

  3. $ \displaystyle 264$ $\displaystyle dm^{2}$

  4. $ \displaystyle 696$ $\displaystyle dm^{2}$

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Correct Option: B
Explanation:

A closed box made by steel with uniform thickness length 12 dm ,breath  10 dm and 8 dm and thickness  of steel is 1 dm

Then inner length =12-2=10 dm ,breadth=10-2=8 dm and height=8-2=6 dm 
So surface area of box=$2(lw+wh+lh)=2(10\times 8)+(8\times 6)+(10\times 6)=2(80+48+60)=2\times 188=376 dm ^{2}$

Consider a rectangle of perimeter $24\ cm$ with sides $a$ and $b$. Then the total number of square grids formed in that rectangle is given by

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $a\times b$

  2. $a+b$

  3. $a-b$

  4. $\dfrac{a}{b}$

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Correct Option: A
Explanation:
Area of rectangle$=a\times b$
Area of $1$ square grid$=1 cm^2$
No. of square grids$=\cfrac { a\times b }{ 1 } =a\times b$

Form a rectangle with $8$ square grids where each square grid measure $1\ cm^{2}$. Find the total area of the rectangle.

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $8\ cm^{2}$

  2. $12\ cm^{2}$

  3. $16\ cm^{2}$

  4. $20\ cm^{2}$

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Correct Option: A
Explanation:

Area of rectangle$=8\times $ area of $1$ square grid$=8\times 1=8 cm^2$

Let there be a rectangle of area $24\ cm^{2}$. Then find the total number of square grids made in this rectangle.(Each square grid measures $1\ cm^{2}$)

maths spaces and boundaries - 2 area of rectangular paths comparing areas problems on areas

  1. $3$

  2. $6$

  3. $12$

  4. $24$

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Correct Option: D
Explanation:

Number of square grids$=\cfrac { Area\quad of\quad rectangle }{ area\quad of\quad square\quad grid } =\cfrac { 24 }{ 1 } =24$