How do you use Heron's formula to find the area of a triangle with sides of lengths #7 #, #4 #, and #6 #?
Let a, b, c be the sides of the triangle. Calculate the semi-perimeter s = (a+b+c)/2. Heron's formula for the area is
By signing up, you agree to our Terms of Service and Privacy Policy
To use Heron's formula to find the area of a triangle with sides of lengths (a), (b), and (c), where (s) is the semiperimeter (half of the perimeter), you follow these steps:
-
Calculate the semiperimeter (s) using the formula: [s = \frac{a + b + c}{2}.]
-
Then, use Heron's formula: [Area = \sqrt{s(s-a)(s-b)(s-c)}.]
For the given triangle with side lengths (a = 7), (b = 4), and (c = 6), we first find the semiperimeter (s): [s = \frac{7 + 4 + 6}{2} = \frac{17}{2} = 8.5.]
Now, plug the values into Heron's formula: [Area = \sqrt{8.5(8.5-7)(8.5-4)(8.5-6)}.]
[= \sqrt{8.5(1.5)(4.5)(2.5)}.]
[= \sqrt{8.5(1.5)(4.5)(2.5)}.]
[= \sqrt{229.6875}.]
[= 15.134.]
So, the area of the triangle is approximately (15.134) square units.
By signing up, you agree to our Terms of Service and Privacy Policy
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.
- A cone has a height of #6 cm# and its base has a radius of #6 cm#. If the cone is horizontally cut into two segments #2 cm# from the base, what would the surface area of the bottom segment be?
- The lengths of the sides of a triangle are in the ratio 5 : 6 : 7. What is the length of the longest side if the perimeter is less than 54 cm?
- The base of a triangular pyramid is a triangle with corners at #(6 ,5 )#, #(7 ,1 )#, and #(4 ,7 )#. If the pyramid has a height of #7 #, what is the pyramid's volume?
- How do you use Heron's formula to find the area of a triangle with sides of lengths #15 #, #16 #, and #12 #?
- A chord with a length of #4 # runs from #pi/3 # to #pi/2 # radians on a circle. What is the area of the circle?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7