To find the area of a triangle with sides of lengths 4 cm, 7 cm, and 9 cm, we can use Heron's formula which is useful when you know all three sides of the triangle. The formula is:
Area = √(s * (s - a) * (s - b) * (s - c))
where a, b, and c are the lengths of the sides of the triangle, and s is the semi-perimeter of the triangle. The semi-perimeter is half of the perimeter of the triangle.
Step 1: Calculate the semi-perimeter (s) using the lengths of the sides:
s = (a + b + c) / 2
s = (4 + 7 + 9) / 2
s = 20 / 2
s = 10
Step 2: Plug a, b, c, and s into Heron's formula to find the area:
Area = √(s * (s - a) * (s - b) * (s - c))
Area = √(10 * (10 - 4) * (10 - 7) * (10 - 9))
Area = √(10 * 6 * 3 * 1)
Area = √(180)
Step 3: Calculate the square root:
Area = √(180) = √(9 * 20) = √(9) * √(20) = 3 * √(4 * 5) = 3 * 2 * √5
Area = 6 * √5
Step 4: Since we want to find the area correct to one decimal place, we need to calculate the numerical value of 6 * √5.
5 under the square root is approximately 2.236.
Therefore, Area ≈ 6 * 2.236.
Area ≈ 13.416
Step 5: Round to one decimal place:
Area ≈ 13.4 cm²
So the area of the triangle is approximately 13.4 square centimeters.
