Q. 5 C5.0( 1 Vote )

Let us draw the squares whose areas equal to the areas of the following triangles:

An equilateral triangle whose side is 6cm. in length.

Answer :

Steps of construction:


1) Draw a triangle PQR with sides PQ = QR = PR = 6 cm.



2) Draw a rectangle ARCP with area equal to that of triangle PQR, by choosing length of rectangle as half of base and height same as height of triangle.


[Here, area of rectangle = length × breadth


= 1/2 × base × height


= area of triangle]


Now, we can make a square with area equal to that of rectangle and hence equal to area of triangle.



3) Extend CP to CE, such that CE = BC



4) Draw the perpendicular bisector of PE which bisects PE at O.



5) Taking O as center and OD = OE as radius, draw a semicircle.



6) Extend BC which intersects semicircle at F.



7) Draw a square CFGH taking CF as side.



Here,


Area of square CFGH = area of rectangle ABCD


= area of ΔPQR


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