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Chapter 4: Q. 1 (page 327)

Given formula for the areas of each of the following geometric figures
a) area of circle with radius r
b) a semicircle of radius r
c) a right triangle with legs of lengths a and b
d) a triangle with base b and altitude h
e) a rectangle with sides of lengths w and l
f) a trapezoid with width w and height $h_{1}, h_{2}$

Short Answer

Expert verified

The areas can be given as

$a) a r e a o f c i r c l e w i t h r a d i u s r = 蟺 r^{2} b) a s e m i c i r c l e o f r a d i u s r = \frac{蟺 r^{2}}{2} c) a r i g h t t r i a n g l e w i t h l e g s o f l e n g t h s a a n d b = \frac{1}{2} 路 a 路 b d) a t r i a n g l e w i t h b a s e b a n d a l t i t u d e h = \frac{1}{2} 路 b 路 h e) a r e c \tan g l e w i t h s i d e s o f l e n g t h s w a n d l = w 路 l f) a t r a p e z o i d w i t h w i d t h w a n d h e i g h h_{1}, h_{2} = \frac{1}{2} 路 w (h_{1} + h_{2})$

Step by step solution

01

Given information

We are given geometric figures we have to find their areas

02

Give the formulas

We have,

$a) a r e a o f c i r c l e w i t h r a d i u s r = 蟺 r^{2} b) a s e m i c i r c l e o f r a d i u s r = \frac{蟺 r^{2}}{2} c) a r i g h t t r i a n g l e w i t h l e g s o f l e n g t h s a a n d b = \frac{1}{2} 路 a 路 b d) a t r i a n g l e w i t h b a s e b a n d a l t i t u d e h = \frac{1}{2} 路 b 路 h e) a r e c \tan g l e w i t h s i d e s o f l e n g t h s w a n d l = w 路 l f) a t r a p e z o i d w i t h w i d t h w a n d h e i g h h_{1}, h_{2} = \frac{1}{2} 路 w (h_{1} + h_{2})$

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