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How do you use Heron's formula to find the area of a triangle with sides of lengths #11 #, #14 #, and #18 #?

Answer 1

Sophia Alfred

#Area=76.98# square units

Hero's formula for finding area of the triangle is given by #Area=sqrt(s(s-a)(s-b)(s-c))#

Where #s# is the semi perimeter and is defined as #s=(a+b+c)/2#

and #a, b, c# are the lengths of the three sides of the triangle.

Here let #a=11, b=14# and #c=18#

#implies s=(11+14+18)/2=43/2=21.5#

#implies s=21.5#

#implies s-a=21.5-11=10.5, s-b=21.5-14=7.5 and s-c=21.5-18=3.5# #implies s-a=10.5, s-b=7.5 and s-c=3.5#

#implies Area=sqrt(21.5*10.5*7.5*3.5)=sqrt5925.9375=76.98# square units

#implies Area=76.98# square units

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Answer 2

Theodore Abad

To use Heron's formula to find the area of a triangle with sides of lengths 11, 14, and 18, you first calculate the semi-perimeter (s) using the formula: s = (a + b + c) / 2, where a, b, and c are the lengths of the sides.

In this case, a = 11, b = 14, and c = 18.

s = (11 + 14 + 18) / 2 = 43 / 2 = 21.5

Then, use Heron's formula: Area = √(s(s - a)(s - b)(s - c))

Area = √(21.5(21.5 - 11)(21.5 - 14)(21.5 - 18))

Area = √(21.5 * 10.5 * 7.5 * 3.5)

Area ≈ √(2477.8125)

Area ≈ 49.77 square units

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.