Question

PQRS is a parallelogram (see the given figure). QM is the height from Q to SR and QN is the height from Q to PS. If SR = \(12\) cm and QM = \(7.6\) cm. Find: 

1. the area of the parallelogram PQRS 
2.  QN, if PS = 8 cm

Answer 1

(a) \(\text{Area of parallelogram} = \text{Base }× \text{Height }\)
= \(SR × QM\)
= \(7.6 × 12 = 91.2 \;cm^2\)

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(b) \(\text{Area of parallelogram} = \text{Base }× \text{Height }\) 
= \(PS × QN\) 
= \(91.2 \;cm^2\)
\(\Rightarrow QN × 8 = 91.2\)
\(\Rightarrow QN = \frac{91.2}{8}=11.4\;cm\)