construct a trapezium PQRS in which PQ//SR, angle P=105 degree, PS=3cm,PQ=4cm,RQ=4.5cmand RS=8cm.
Answers
Answer:
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Answer:
Given:
PQ
is parallel to
SR
, PQ = 8 cm, ∠ PQR = 70
o
QR = 6 cm and PS = 6 cm.
Steps for construction
Step 1 : Draw a rough diagram and mark the given measurements.
Step 2 : Draw a line segment PQ = 8 cm.
Step 3 : At Q on
PQ
make ∠ PQX whose measure is 70
o
.
Step 4 : With Q as centre and 6 cm as radius draw an arc. This cuts $$\overline{QX}$$ at R.
Step 5 : Draw
RY
parallel to
OP
.
Step 6 : With Q as centre and radius 6 cm draw an arc cutting
RY
at S.
Step 7 : Join
PS
. PQRS is the required trapezium.
Step 8 : From S draw
ST
⊥
PQ
and measure the length of ST. ST = h = 5.6 cm, RS = b = 6 cm, PQ = a = 8 cm.
Calculation of area:
In the trapezium PQRS, a = 8 cm, b = 3.9 cm and h = 5.6 cm.
Area of the trapezium ABCD =
2
1
h(a+b)
=
2
1
(5.6)(8+3.9)
=
2
1
× 5.6×11.9
=33.32 cm
2
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Step-by-step explanation: