How do you use Heron's formula to find the area of a triangle with sides of lengths #9 #, #5 #, and #11 #?

Answer 1

≈ 22.185

This is a two step process

step 1 : Find half the perimeter (s) of the triangle

step 2 : calculate the area (A)

let a = 9 , b = 5 and c = 11

step 1 : s #= (a+b+c)/2 = (9+5+11)/2 = 25/2 = 12.5 #
step 2 : #A = sqrt(s(s-a)(s-b)(s-c))#
# = sqrt(12.5(12.5-9)(12.5-5)(12.5-11))#
#rArr A = sqrt(12.5xx3.5xx7.5xx1.5) ≈ 22.185#
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Answer 2

To use Heron's formula to find the area of a triangle with sides of lengths 9, 5, and 11, follow these steps:

  1. Calculate the semi-perimeter (s) of the triangle using the formula: s = (a + b + c) / 2, where a, b, and c are the lengths of the sides of the triangle.

  2. Once you have the semi-perimeter (s), use Heron's formula to find the area (A) of the triangle: A = √(s * (s - a) * (s - b) * (s - c)), where s is the semi-perimeter, and a, b, and c are the lengths of the sides of the triangle.

  3. Substitute the given side lengths into the formulas: a = 9, b = 5, c = 11.

  4. Calculate the semi-perimeter: s = (9 + 5 + 11) / 2 = 25 / 2 = 12.5

  5. Substitute the semi-perimeter and side lengths into Heron's formula: A = √(12.5 * (12.5 - 9) * (12.5 - 5) * (12.5 - 11))

  6. Perform the calculations: A = √(12.5 * 3.5 * 7.5 * 1.5) A = √(367.96875)

  7. Simplify: A ≈ √(367.96875) ≈ 19.21

Therefore, the area of the triangle with side lengths 9, 5, and 11 is approximately 19.21 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.

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.

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.

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.

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