side of a equilateral triangle is =16cm .Find its area and height also.step by step solution please.
Answers
s=16+16+16/2
s=48/2
s=24
area=square root{s(s-a)(s-b)(s-c)
= square root{24(24-16)(24-16)(24-16)
= square root{24×8×8×8}
=
64root3
area of triangle=1/2×base×height
64root3=1/2×16×h
8root3=h
Answer: the answers are:
area:64√3
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altitude:8√3
Step-by-step explanation: As the area of equilateral triangle is:√3/4 a²
where a is one side.
so,
area=√3/4 .(16)²
√3/4.256
area=64√3
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construction: draw an median AD to triangle ABC.
pf: so we get the right angled triangle ADC right angled at D. median AD is also the altitude or height.
:. WE ARE GIVEN THAT AC=16. SO AD=8cm(as ADis the median it divides the base into two equal parts.)
by pythagoraus theorem
AB²=AD²+BD²
AD²=16²-8²=256-64=192
AD=√192=√8×24=taking out 8 as common and we know that 8×3 is equal to 24 so under root 3 is left and 8 taken as common is present outside=8√3
therefore the height is 8√3