find the area and the side of the height of an equilateral triangle whose each side measures:
i) 12cm.
ii) 10m.
iii) 6.4m (take square root=3 ,=1.73 in each case.
more book information:- book- foundation mathematics R.S. Aggarwal . 7th grade.
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Answer:
To find the area and the height of an equilateral triangle, you can use the following formula:
Area (A) = (sqrt(3) / 4) * side^2
Height (h) = (sqrt(3) / 2) * side
Now, let's calculate for each case:
i) Side = 12 cm
Area (A) = (sqrt(3) / 4) * (12 cm)^2 = (sqrt(3) / 4) * 144 cm^2 = 36 sqrt(3) cm^2
Height (h) = (sqrt(3) / 2) * 12 cm = 6 sqrt(3) cm
ii) Side = 10 m
Area (A) = (sqrt(3) / 4) * (10 m)^2 = (sqrt(3) / 4) * 100 m^2 = 25 sqrt(3) m^2
Height (h) = (sqrt(3) / 2) * 10 m = 5 sqrt(3) m
iii) Side = 6.4 m
Area (A) = (sqrt(3) / 4) * (6.4 m)^2 = (sqrt(3) / 4) * 40.96 m^2 = 10.24 sqrt(3) m^2
Height (h) = (sqrt(3) / 2) * 6.4 m = 3.2 sqrt(3) m
So, for the given side lengths:
i) Area is 36 sqrt(3) square centimeters, and the height is 6 sqrt(3) centimeters.
ii) Area is 25 sqrt(3) square meters, and the height is 5 sqrt(3) meters.
iii) Area is 10.24 sqrt(3) square meters, and the height is 3.2 sqrt(3) meters.
Answer:
To find the area (A) and height (h) of an equilateral triangle, you can use the following formulas:
A = (sqrt(3) / 4) * s^2
h = (sqrt(3) / 2) * s
Where:
- A is the area of the equilateral triangle.
- h is the height of the equilateral triangle.
- s is the length of each side of the equilateral triangle.
Let's calculate for each case:
i) When each side measures 12 cm:
A = (sqrt(3) / 4) * (12 cm)^2 = (sqrt(3) / 4) * 144 cm^2 = 36 sqrt(3) cm^2
h = (sqrt(3) / 2) * 12 cm = 6 sqrt(3) cm
ii) When each side measures 10 m:
A = (sqrt(3) / 4) * (10 m)^2 = (sqrt(3) / 4) * 100 m^2 = 25 sqrt(3) m^2
h = (sqrt(3) / 2) * 10 m = 5 sqrt(3) m
iii) When each side measures 6.4 m:
A = (sqrt(3) / 4) * (6.4 m)^2 = (sqrt(3) / 4) * 40.96 m^2 = 10.24 sqrt(3) m^2
h = (sqrt(3) / 2) * 6.4 m = 3.2 sqrt(3) m
These are the correct answers for the area and height of the equilateral triangle for each case.