In the parallelogram PQRS above , PS=7 cm, PQ=3cm and angle PQS=100°
Calculate to the nearest whole number, the magnitude of angle PSQ
Answers
Step-by-step explanation:
Maths
Practical Geometry
Construction of Quadrilaterals
Construct a quadrilateral P...
MATHS
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.
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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
solution