Find the perimeter and area of the triangle.
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Question content area top right
Part 1
21.3 cm
10.1 cm
17.1 cm
8 cm
Question content area bottom
Part 1
The perimeter
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(Be sure to include the correct units.)
To find the perimeter of the triangle, we need to add up the lengths of all three sides.
Perimeter = 21.3 cm + 10.1 cm + 17.1 cm = 48.5 cm
Now, let's find the area of the triangle using Heron's formula:
Step 1: Find the semi-perimeter (s) = (a + b + c) / 2
s = (21.3 + 10.1 + 17.1) / 2 = 48.5 / 2 = 24.25 cm
Step 2: Use Heron's formula
Area = √(s * (s - a) * (s - b) * (s - c))
Area = √(24.25 * (24.25 - 21.3) * (24.25 - 10.1) * (24.25 - 17.1))
Area = √(24.25 * 2.95 * 14.15 * 7.15)
Area = √(1026.23)
Area ≈ 32.03 cm²
So, the perimeter of the triangle is 48.5 cm and the area is approximately 32.03 cm².