question_answer 1)

PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If \[\text{SR}=\text{12 cm}\] and \[\text{QM}=\text{7}.\text{6}\] cm. Find: (a) the area of the parallelogram PQRS      (b) \[QN,\]if \[\text{PS = 8 cm}\].                  

Answer:

                (a) Area of the parallelogram PQRS                         \[\text{= base  }\!\!\times\!\!\text{  height = SR  }\!\!\times\!\!\text{  QM}\] \[\text{= 12  }\!\!\times\!\!\text{  7}\text{.6 c}{{\text{m}}^{\text{2}}}\text{ = 91}\text{.2 c}{{\text{m}}^{\text{2}}}\] (b) Area of the parallelogram PQRS \[=\text{base}\times \text{height}=\text{PS}\times \text{QN}\]                 \[\Rightarrow \]               \[\text{91}\text{.2 = 8  }\!\!\times\!\!\text{  QN}\]                 \[\Rightarrow \]               \[\text{QN =}\frac{\text{91}\text{.2}}{\text{8}}\text{ cm}\]                 \[\Rightarrow \]               \[\text{QN = 11}\text{.4 cm}\text{.}\]