Question

Find the area of the trapezium
PRTS, given that the side ST of the
parallelogram PQTS is 28 cm, side
QT = 10 cm, TR = 10 cm and TM = 6 cm.
S
28 cm
T
10 cm
10 cm
6 cm
PR
M
Q​

Answer 1

Answer:

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}RM=(RT)2−(TM)2

Put the value into the formula

RM=\sqrt{(10)^2-(6)^2}RM=(10)2−(6)2

RM=8\ cmRM=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\ RTQA=Area of parallelogram PQTS−Area of triangle RTQ

A=h\times b-\dfrac{1}{2}\times b\times hA=h×b−21×b×h

Put the value into the formula

A=28\times6-\dfrac{1}{2}\times16\times6A=28×6−21×16×6

A=120\ cm^2A=120 cm2

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