In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, what is the area of th

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Question: In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, what is the area of the triangle?

Options:

Correct Answer: 30 cm²

Solution:

Using Heron\'s formula, s = (8 + 6 + 10) / 2 = 12 cm. Area = √[s(s-a)(s-b)(s-c)] = √[12(12-8)(12-6)(12-10)] = √[12*4*6*2] = √144 = 12 cm².

In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, what is the area of the triangle?

In triangle DEF, if DE = 8 cm, EF = 6 cm, and DF = 10 cm, what is the area of the triangle?

Step 1: Identify the lengths of the sides of triangle DEF. They are DE = 8 cm, EF = 6 cm, and DF = 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 lengths of the sides.
Step 3: Substitute the values into the formula: s = (8 + 6 + 10) / 2 = 24 / 2 = 12 cm.
Step 4: Use Heron's formula to find the area of the triangle. The formula is Area = √[s(s-a)(s-b)(s-c).
Step 5: Substitute the values into Heron's formula: Area = √[12(12-8)(12-6)(12-10)].
Step 6: Calculate each part: (12-8) = 4, (12-6) = 6, (12-10) = 2.
Step 7: Now substitute these values back into the formula: Area = √[12 * 4 * 6 * 2].
Step 8: Calculate the product: 12 * 4 = 48, then 48 * 6 = 288, and finally 288 * 2 = 576.
Step 9: Find the square root of 576: Area = √576 = 24 cm².
Step 10: The area of triangle DEF is 24 cm².

Heron's Formula – A method to calculate the area of a triangle when the lengths of all three sides are known.
Semi-perimeter – The semi-perimeter (s) is half the sum of the triangle's side lengths, used in Heron's formula.