()
P
4 cm
.
7 cm x
Х
3 cm
S
R
Answers
Answer:
8th
Maths
Practical Geometry
Construction of Quadrilaterals
Construct a quadrilateral P...
MATHS
Asked on December 26, 2019 by
Manju Bhosale
Construct a quadrilateral PQRS with PQ = 4 cm, QR = 6 cm, PR = 7 cm, PS = 5 cm and ∠ PQS = 40
o
and find its area.
MEDIUM
ANSWER
Given:
PQ = 4 cm, QR = 6 cm, PR= 7 cm, PS= 5 cm and ∠ PQS = 40.
Steps for construction
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment PQ = 4 cm.
Step 3 : With P and Q as centres draw arcs of radii 7 cm and 6 cm respectively and let them cut at R.
Step 4 : Join
PR
and
QR
.
Step 5 : At Q on
PQ
make ∠ PQT whose measure is 40
o
.
Step 6 : With P as centre and radius 5 cm draw an arc. This cuts
QT
at S.
Step 7 : Join
PS
. PQRS is the required quadrilateral.
Step 8 : From Q draw
QX
⊥
PR
and from S draw
SY
⊥
PR
. Measure the lengths QX and SY. QX = h
1
= 3.1 cm, SY = h
2
= 3.9 cm. PR = d = 7 cm.
Calculation of area:
In the quadrilateral ABCD, d = 7 cm, h
1
= 3.1 cm and h
2
= 3.9 cm.
Area of the quadrilateral ABCD =
2
1
d(h
1
+h
2
)
=
2
1
(7)(3.1+3.9)
=
2
1
×7×7
=24.5cm
2
Answer By
Toppr
Prev Question
Next Question
Related Questions to study
Construct a cyclic quadrilateral PQRS with PQ=4cm, QR=6cm, PR=7.5cm, QS=7cm.
View Answer
Construct a quadrilateral PQRS in which PQ=3.8 cm, QR=3.4 cm, RS=4.5 cm, SP=5 cm and ∠Q=80
o
. State which of these is the last step.
View Answer
VIEW MORE
Revise with Concepts
Specifying a Quadrilateral
EXAMPLE
DEFINITIONS
FORMULAES
Quick summary with Stories
Essential Conditions for Construction of a Quadrilateral
2 mins read
Construction of a Basic Quadrilateral.
2 mins read