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10 grade maths

Find the area of the triangle with 5 cm, 12 cm, 13 cm.

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10 Months agoGrade
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1 Answer

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ApprovedApproved Tutor Answer9 Months ago

To find the area of a triangle with sides measuring 5 cm, 12 cm, and 13 cm, we can use Heron's formula. This formula is useful when we know the lengths of all three sides.

Step 1: Calculate the Semi-Perimeter

The semi-perimeter (s) is calculated as follows:

  • First, add the lengths of the sides: 5 cm + 12 cm + 13 cm = 30 cm
  • Then, divide by 2: s = 30 cm / 2 = 15 cm

Step 2: Apply Heron's Formula

Heron's formula for the area (A) is:

A = √(s × (s - a) × (s - b) × (s - c))

Where a, b, and c are the lengths of the sides. Plugging in the values:

  • A = √(15 × (15 - 5) × (15 - 12) × (15 - 13))
  • A = √(15 × 10 × 3 × 2)
  • A = √(900)
  • A = 30 cm²

Final Result

The area of the triangle is 30 square centimeters.

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