Construct a quadrilateral PQRS, in which PQ = 4 cm, PR = 6 cm, PS = 10 cm and angle PQR and angle QRS both are right angle.
Answers
Step-by-step explanation:
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 40o .
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 = h1 = 3.1 cm, SY = h2 = 3.9 cm. PR = d = 7 cm.
Calculation of area:
In the quadrilateral ABCD, d = 7 cm, h1 = 3.1 cm and h2 = 3.9 cm.
Area of the quadrilateral ABCD = 21d(h1+h2)
=21(7)(3.1+3.9)
=21×7×7
=24.5cm2