A, B. C and D are the respective mid-points of the sides PQ. QR, RS and PS of quadrilateral PQRS. If PR = 20 cm and QS =
16 cm, then what is the perimeter of quadrilateral ABCD?
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Answer:
36 cm
Step-by-step explanation:
Please refer to the attached figure
In the figure,
SPQ is a Δ.
Points D and A are the midpoints of sides SP and PQ of the triangle.
Hence we can use the Midpoint Theorem which states:
The line joining the midpoints of any two sides of a triangle is parallel to and half of the third side.
∴AD = 1/2(QS)
= 8cm (i)
Similarly, for ΔSRQ,
BC = 1/2(QS)
= 8cm (ii)
Now,
PQR is a triangle,
Applying the Mid-point theorem,
AB = 1/2(PR)
=10 cm (iii)
Similarly for ΔPSR,
CD = 1/2(PR)
= 10 cm (iv)
Perimeter of the quadrilateral
= AD + BC + AB + CD
= 8 + 8 + 10 + 10 ( From (i), (ii), (iii) and (iv) )
= 36 cm
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