A triangle with base b and height h has area A = 1/2 bh. If the base is doubled and the height halved, what happens to the area?

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Prepare for the AMSOC 26-003 Module A Test. Utilize flashcards and multiple choice questions with hints and explanations. Ace your exam!

Multiple Choice

A triangle with base b and height h has area A = 1/2 bh. If the base is doubled and the height halved, what happens to the area?

Explanation:
When you scale the base by 2 and the height by 1/2, the area changes by the product of those factors. Since 2 × (1/2) = 1, the area stays the same. Using the area formula: A' = 1/2 × (2b) × (h/2) = 1/2 × 2b × h/2 = 1/2 × b × h = A. For a quick check, if b = 6 and h = 4, A = 12. After doubling the base and halving the height, you get base 12 and height 2, so A' = 1/2 × 12 × 2 = 12.

When you scale the base by 2 and the height by 1/2, the area changes by the product of those factors. Since 2 × (1/2) = 1, the area stays the same.

Using the area formula: A' = 1/2 × (2b) × (h/2) = 1/2 × 2b × h/2 = 1/2 × b × h = A.

For a quick check, if b = 6 and h = 4, A = 12. After doubling the base and halving the height, you get base 12 and height 2, so A' = 1/2 × 12 × 2 = 12.

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