find the area of equilateral triangle having height square root six
Answers
GIVEN: Triangle ABC is an equilateral triangle.
Altitude CM = √6
TO FIND THE AREA: of equilateral triangle ABC
Here Sin60° ,= CM/CB
=> √3/2 = √6/CB
=> √3 CB = 2√6
=> CB = 2√6 / √3
=> CB = 2√2
=> AB = 2√2
Area( triangle ABC) = 1/2 * AB * CM
=> Area( triangle ABC) = 1/2 * 2√2 * √6
=> Area(triangle ABC) = √12 = 2√3
Ans: 2√3 sq unit
Justification:
Since Area( tri ABC) = ar( tri CMB) + ar( tri CMA)
= (1/2 * √2 * √6 ) + ( 1/2 * √2 * √6)
= √12/2 + √12/2
= (2√12)/2
= √12 = 2√3 sq unit
Answer:
Step-by-step explanation:
Altitude of equilateral triangle = √3/2 * side
√6 = √3/2 * side
side = √6 * 2 / √3 = 2.807
Area of equi. triangle = √3/4 * side²
= √3/4 * 2.807²
= √3/4 * 7.87
= 0.4345 * 7.87 = 3.419 unit²