A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. What is its area?

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Question: A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. What is its area?

Options:

Correct Answer: 30 cm²

Solution:

This is a right triangle. Area = (base × height) / 2 = (5 cm × 12 cm) / 2 = 30 cm².

A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. What is its area?

A triangle has sides of lengths 5 cm, 12 cm, and 13 cm. What is its area?

Step 1: Identify the lengths of the sides of the triangle. They are 5 cm, 12 cm, and 13 cm.
Step 2: Check if the triangle is a right triangle. Use the Pythagorean theorem: a² + b² = c², where c is the longest side.
Step 3: Calculate 5² + 12². This equals 25 + 144 = 169.
Step 4: Calculate 13². This equals 169.
Step 5: Since 5² + 12² equals 13², the triangle is a right triangle.
Step 6: Identify the base and height. We can use 5 cm as the base and 12 cm as the height.
Step 7: Use the formula for the area of a triangle: Area = (base × height) / 2.
Step 8: Substitute the values: Area = (5 cm × 12 cm) / 2.
Step 9: Calculate the area: 5 cm × 12 cm = 60 cm².
Step 10: Divide by 2: 60 cm² / 2 = 30 cm².
Step 11: The area of the triangle is 30 cm².

Right Triangle Identification – Recognizing that a triangle with sides 5 cm, 12 cm, and 13 cm is a right triangle based on the Pythagorean theorem.
Area Calculation – Using the formula for the area of a triangle, specifically for right triangles, which is (base × height) / 2.