Q. 1 - Calculus | StudyQuestionHub

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Q. 1

Question

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 $h_{1}, h_{2}$

Step-by-Step Solution

Verified

Answer

The areas can be given as

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

1Step 1: Given information

We are given geometric figures we have to find their areas

2Step 2: Give the formulas

We have,

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

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