Question

In the given figure,LMN is a right angled triangle in which m=90°,P and Q are mid points of LM and LN respectively.If LM=9 cm,MN=12 cm and LN=15 cm,find:

1. the perimeter of trapezium MNQP
2.the area of trapezium MNQP​

Answer 1

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✌️ PLZ CHECK ATTACHMENT ✌️

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Answer 2

1.The perimeter of trapezium MNQP=30 cm

2.The area of trapezium MNQP=40.5 square cm

Step-by-step explanation:

In right triangle LMN,

$\angle M=90^{\circ}$

LM=9 cm

MN=12 cm

LN=15 cm

P is the mid point of LM

Therefore, LP=PM=$\frac{1}{2}LM=\frac{9}{2}=4.5$ cm

LQ=QN=$\frac{1}{2}LN=\frac{1}{2}\times 15$=7.5 cm

By mid- segment theorem

$PQ=\frac{1}{2}MN$,$PQ\parallel MN$

$PQ=\frac{1}{2}(12cm)=6 cm$

1.Perimeter of trapezium=PM+MN+QN+PQ=4.5+12+7.5+6=30 cm

2.Area of trapezium PMNQ=$\frac{1}{2}(sum\;of\;parallel\;sides)\times h$

Area of trapezium PMNQ=$\frac{1}{2}(6+12)\times 4.5$

Area of trapezium PMNQ=$9\times 4.5=40.5cm^2$

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