Question

find the area of the trapezium PRTS,given that the side ST of the parallelogram PQTS is 28cm, side QT=10cm ,TR=10cm and TM=6cm.

Answer 1

Given that,

Side of ST = 28 cm

Side of QT = 10 cm

Side of TR = 10 cm

Side of TM = 6 cm

We need to calculate the value of RQ

Using pythagorean theorem,

$RM=\sqrt{(RT)^2-(TM)^2}$

Put the value into the formula

$RM=\sqrt{(10)^2-(6)^2}$

$RM=8\ cm$

So, The value of RQ will be 16 cm.

We need to calculate the area of the trapezium PRTS

Using formula of area

$A=Area\ of\ parallelogram\ PQTS-Area\ of\ triangle\ RTQ$

$A=h\times b-\dfrac{1}{2}\times b\times h$

Put the value into the formula

$A=28\times6-\dfrac{1}{2}\times16\times6$

$A=120\ cm^2$

Hence, The area of the trapezium PRTS is 120 cm².