Tag: region enclosed by a plane figure

Questions Related to region enclosed by a plane figure

One side of a square is $4$ ft long. What is its area?

maths perimeter and area of rectilinear figures region enclosed by a plane figure area of square and rectangle mensuration-i (area)

  1. 6 $ft^2$

  2. 4$ft^2$

  3. 8 $ft^2$

  4. 16 $ft^2$

Show answer
Correct Option: D
Explanation:

Area of a square = $side \times  side$
one side = 4 ft
Area = $4^2$
Area = $16$ $ft^2$

The perimeter of a rhombus is 100 cm and one of the diagonals is 40 cm, Then the area of the rhombus is

maths perimeter and area of rectilinear figures region enclosed by a plane figure area of square and rectangle mensuration-i (area)

  1. 1000 cm$^2$

  2. 500 cm$^2$

  3. 1200 cm$^2$

  4. 600 cm$^2$

Show answer
Correct Option: D
Explanation:

Given that, perimeter of rhombus is $100cm$ and one diagonal $40cm$

Perimeter of rhombus=4$\times $side

So side$=25cm$

And we know that in a rhombus diagonal divides rhombus in two eauilateral triangle.

Area of one triangle:- s$=(25+25+40)/2 =45$

So area=(s$\times $(s-a)$\times $ (s-b)$\times $(s-c))^1/2

= (45$\times $(45-40)$\times $(45-25)$\times $(45-25))^1/2

$= 300cm^2$

So total area is 300$\times $2=600cm^2

 

Hence, this is the answer.