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

Simple interest, find the simple interest on Rs. 68,000 at 50/3 per annum f...

find the simple interest on Rs. 68,000 at 50/3 per annum for 9 month

Evaluate of the largest angle, The measures of the angles of a triangle are...

The measures of the angles of a triangle are in the ratio of 3:4:5. Evaluate of the largest angle. a. 75° b. 37.5° c. 45° d. 60° a. The addition of the measures of t

Three set problems, In a class,there are 174 students in form three,86 stud...

In a class,there are 174 students in form three,86 students play table tennis,84 play football and 94 play volleyball,30 play table tennis and volleyball,34 play volleyball and foo

Example of distributive law, Maya gives the children examples of distributi...

Maya gives the children examples of distributive with small numbers initially, and leads them towards discovering the law. The usual way she does this is to give the children probl

solve the game by linear programming, UA and DU are preparing for the NCAA...

UA and DU are preparing for the NCAA basketball game championship. They are setting up their strategies for the championship game. Assessing the strength of their "benches", each c

Real analysis, .find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd a...

.find lim sup Ek and liminf Ek of Ek=[(-(1/k),1] for k odd and liminf Ek=[(-1,(1/k)] for k even

Example of adding signed numbers, Example of Adding signed numbers: E...

Example of Adding signed numbers: Example: (2) + (-4) =      Solution: Start with 2 and count 4 whole numbers to the left. Thus: (2) + (-4) = -2 Adding

How many miles will he jog in 30 minutes, Mike can jog 6.5 miles per hour. ...

Mike can jog 6.5 miles per hour. At this rate, how many miles will he jog in 30 minutes? Thirty minutes is half an hour. Thus, divide the number of miles Mike can jog in one ho

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