Find the area of the shaded region of square, Mathematics

Assignment Help:

In the adjoining figure, ABCD is a square of side 6cm.  Find the area of the shaded region.

1190_circle33.png

Ans:    From P draw PQ ⊥ AB

AQ = QB = 3cm

(Ans: 34.428 sq cm)

Join PB. Since arc APC is described by a circle with center B,

so BA = BP=BC =6cm.

In ? PQB Cos θ  = QB/PB  = 1/2

∴θ     = 60o

Area of sector BPA =60/360 Π (62) = 18.84cm

Area of  Δ BPQ = 1/2(QB) (PQ) = 1/2 (3)( 6 Sin 60) = 7.794Sq.cm

Area of portion APQ = Area of sector BPA - Area of  Δ BPQ

= 18.84 - 7.794 = 11.046 Sq.cm

Area of shaded portion = 2 x Area of Quadrant ABC - 2 Area APQ

= [2 x π/4(6)2  - 2 x 11.046]

=34.428 Sq.cm


Related Discussions:- Find the area of the shaded region of square

Number sequence, what is the formula to find a sequence on a string of numb...

what is the formula to find a sequence on a string of numbers?

How would the society be strengthened, All things considered, in a sense of...

All things considered, in a sense of ethnicity (a sense of identification with and loyalty to one's group) good or bad? is it harmful or helpful? What would be lost if Americans lo

Uniform distribution over the interval, High temperatures in certain city i...

High temperatures in certain city in the month of August follow uniform distribution over the interval 60-85 F. What is probability that a randomly selected August day has a Temper

.fractions, what is the difference between North America''s part of the tot...

what is the difference between North America''s part of the total population and Africa''s part

What was the temperature at midnight, The temperature at 6 P.M. was 31°F. T...

The temperature at 6 P.M. was 31°F. Through midnight, it had dropped 40°F. What was the temperature at midnight? Visualize a number line. The drop from 31° to 0° is 31°. There

Hypothesis testing, Hypothesis Testing Definition of Hypothesis Testing...

Hypothesis Testing Definition of Hypothesis Testing - A hypothesis is a claim or an opinion about an issue or item.  Hence it has to be tested statistically in order to esta

Standardizing normal variables, Standardizing Normal Variables Suppose ...

Standardizing Normal Variables Suppose we have a normal population. We can represent it by a normal variable X. Further, we can convert any value of X into a corresponding valu

#perimeter, what are the formulas in finding the perimeter of a plane figur...

what are the formulas in finding the perimeter of a plane figure?

Linear programming , Use the simplex method to solve the following LP Probl...

Use the simplex method to solve the following LP Problem. Max Z = 107x1+x2+2x3 Subject to 14x1+x2-6x3+3x4=7 16x1+x2-6x3 3x1-x2-x3 x1,x2,x3,x4 >=0

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd