Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
2.8k views
in Mensuration by (46.9k points)
closed by

∆ALMN is an equilat triangle. LM = 14 cm. As shown in figure, three sectors are drawn with vertices as centres and radius 7 cm. Find,

i. A (∆ LMN). 

ii. Area of any one of the sectors. 

iii. Total area of all the three sectors. iv. Area of the shaded region. ( √3 = 1.732 )

1 Answer

+3 votes
by (47.6k points)
selected by
 
Best answer

Given: In equilateral triangle LMN, LM =14 cm,

radius of sectors (r) = 7 cm 

i. ∆LMN is an equilateral triangle.

∴  (∆LMN) = √3/4 LM2

= √3/4 x 142

= 49 x 1.732

= 84.868

= 84.87 cm2

.∴  (∆LMN) = 84.87 cm2

ii. Central angle (θ) = 60° …[Angle of an equilateral triangle]

∴ Area of one sector = 25.67 cm2

iii. Total area of all three sectors = 3 × Area of one sector 

= 3 × 25.67 

= 77.01 cm2 

∴ Total area of all three sectors = 77.01 cm2 

iv. Area of shaded region = A(∆LMN) – total area of all three sectors 

= 84.87 – 77.01 

= 7.86 cm2 

∴ Area of shaded region = 7.86 cm2.

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...