Question

construct a quadrilateral pqrs such that pq is 6 cm qr is 4.5 cm rs=ps 5.5cmandpr is 8cm​

Answer 1

Answer:

8th

Maths

Practical Geometry

Construction of Quadrilaterals

Construct a quadrilateral P...

MATHS

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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.

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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

Step-by-step explanation:

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