A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. What is the area of the t

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Question: A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. What is the area of the triangle?

Options:

Correct Answer: 24 cm²

Solution:

Using Heron\'s formula, s = (6 + 8 + 10)/2 = 12. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-6)(12-8)(12-10)] = √[12 × 6 × 4 × 2] = 24 cm².

A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. What is the area of the triangle?

A triangle has sides of lengths 6 cm, 8 cm, and 10 cm. What is the area of the triangle?

Step 1: Identify the lengths of the sides of the triangle. They are 6 cm, 8 cm, and 10 cm.
Step 2: Calculate the semi-perimeter (s) of the triangle using the formula s = (a + b + c) / 2, where a, b, and c are the side lengths. Here, s = (6 + 8 + 10) / 2 = 12 cm.
Step 3: Use Heron's formula to find the area of the triangle. The formula is Area = √[s(s-a)(s-b)(s-c).
Step 4: Substitute the values into the formula. We have s = 12, a = 6, b = 8, and c = 10. So, Area = √[12(12-6)(12-8)(12-10)].
Step 5: Calculate each part inside the square root. First, find (12-6) = 6, (12-8) = 4, and (12-10) = 2.
Step 6: Now substitute these values back into the formula: Area = √[12 × 6 × 4 × 2].
Step 7: Calculate the product: 12 × 6 = 72, then 72 × 4 = 288, and finally 288 × 2 = 576.
Step 8: Take the square root of 576 to find the area. √576 = 24.
Step 9: Therefore, the area of the triangle is 24 cm².

Heron's Formula – A method to calculate the area of a triangle when the lengths of all three sides are known.
Triangle Properties – Understanding the properties of triangles, including the relationship between side lengths and area.