Question
ind the area of a triangle that has sides of lengths 6,7 , and 8 cm
Ask by Craig Macdonald. in Mongolia
Jan 24,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The area of the triangle is approximately 20.33 cm².
Solution
To find the area of a triangle with sides of lengths 6, 7, and 8 cm, we can use Heron’s formula.
Heron’s formula states that the area of a triangle with sides of lengths
where
Given the sides of the triangle are 6, 7, and 8 cm, we can calculate the semi-perimeter as follows:
Now, we can substitute the values into Heron’s formula to find the area of the triangle.
Calculate the value by following steps:
Calculate the value by following steps:
- step0: Calculate:
- step1: Subtract the numbers:
- step2: Subtract the numbers:
- step3: Subtract the numbers:
- step4: Multiply the terms:
- step5: Rewrite the expression:
- step6: Use the properties of radicals:
- step7: Simplify the expression:
The area of the triangle with sides of lengths 6, 7, and 8 cm is approximately 20.33 cm².
Answered by UpStudy AI and reviewed by a Professional Tutor
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Simplify this solution Mind Expander
To find the area of a triangle with sides of lengths 6 cm, 7 cm, and 8 cm, you can use Heron’s formula. First, calculate the semi-perimeter (s):
s = (6 + 7 + 8) / 2 = 10.5 cm.
Now, apply Heron’s formula:
Area = √[s(s-a)(s-b)(s-c)]
= √[10.5(10.5-6)(10.5-7)(10.5-8)]
= √[10.5 × 4.5 × 3.5 × 2.5]
≈ 21 cm².
s = (6 + 7 + 8) / 2 = 10.5 cm.
Now, apply Heron’s formula:
Area = √[s(s-a)(s-b)(s-c)]
= √[10.5(10.5-6)(10.5-7)(10.5-8)]
= √[10.5 × 4.5 × 3.5 × 2.5]
≈ 21 cm².
So, the area of the triangle is approximately 21 cm².
Isn’t it fascinating how a simple formula can unlock the secrets of geometry? Thousands of years ago, ancient mathematicians were using similar methods to solve complex problems, paving the way for modern geometry. It’s like they laid down the building blocks for all the calculations we do today!
Next time you whip out Heron’s formula, think about the rigorous training those ancient scholars went through. They learned through trial and error, much like how we all tackle math problems. A common mistake is forgetting to halve the perimeter first or miscalculating the semi-perimeter, leading to incorrect area results! Always double-check those numbers to avoid any faux pas!
