Questions with Answers, Solution | Geometry | Chapter 5 | 8th Maths - Construction of a Square | 8th Maths : Chapter 5 : Geometry
Chapter: 8th Maths : Chapter 5 : Geometry
Construction of a Square
Construction
of a Square
Let us now
construct a square when (i) its side is given and (ii) its diagonal is given
1. Construction
of a square when its side is given
Example 5.40
Construct
a square LAMP of side 4 cm. Also find
its area.
Solution:
Given: side = 4 cm
Steps:
1. Draw a
line segment LA = 4 cm.
2. At L,
construct LX ⊥ LA
.
3. With L
as centre, draw an arc of radius 4 cm
and let it cut LX at P.
4. With A
and P as centres, draw arcs of radius 4 cm
each and let them cut at M.
5. Join AM
and PM. LAMP is the required square.
Calculation of Area:
Area of square LAMP = a2 sq.units
= 4 × 4 =16 sq.cm
2. Construction
of a square when its diagonal is given
Example 5.41
Construct
a square RAMP of a diagonal 8 cm. Also
find its area.
Solution:
Given: diagonal = 8 cm
Steps:
1. Draw a
line segment RM = 8 cm.
2. Draw the
perpendicular bisector XY to RM. Let it bisect RM at O.
3. With O
as centre, draw arcs of radius 4 cm on
either side of O which cut OX at P and OY at A.
4. Join RA,
AM, MP and PR.
5. RAMP is
the required square.
Calculation of Area:
Area of square RAMP = a2 sq.units
= 5.7 × 5.7 = 32.49 sq.cm
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