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The area of trapezium PQRS given in the figure below is ____ $c m 2$ .

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Detailed Solution

The area of trapezium PQRS given in the figure below is 180

c m 2

.
Given a trapezium PQRS.
Calculate the area of trap. PQRS, given in Fig. - Sarthaks eConnect | Largest Online Education Community

Using Pythagoras Theorem in triangle RQT,

h y p o t e n o u s 2 = b a s e 2 + p e r p e n d i c u l a r 2

R Q 2 = T Q 2 + R T 2 (17) 2 = (8) 2 + R T 2 R T 2 = (17) 2 − (8) 2 R T = 225 R T = 15 cm

Area of rectangle PTRS is,

A = l e n g t h × b r e a d t h A = 8 × 15 A = 120 c m 2

Area of triangle RTQ is,

A = 12 × 8 × 15 A = 1202 A = 60 c m 2

Now, area of trapezium PQRS is,
A = Area of rectangle PTRS + Area of triangle RTQ
A = 120 + 60
A = 180

c m 2

The area of trapezium is 180

c m 2

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