The base of a triangle is 21 inches and the height is 12 inches. Which of these expressions correctly shows how to calculate the area of a triangle?
$(21+12) \div 2$
$(21 \times 12) \times 2$
$(21 \times 12) \div 2$
$(21+12) \times 2$
Answer (2)
The area of a triangle is calculated using the formula: Area = 2 1 × base × height .
Substitute the given base (21 inches) and height (12 inches) into the formula: Area = 2 1 × 21 × 12 .
Rewrite the expression: Area = ( 21 × 12 ) ÷ 2 .
The correct expression for the area of the triangle is: ( 21 × 12 ) ÷ 2 .
Explanation
Understanding the problem and formula The area of a triangle is calculated using the formula: Area = (1/2) * base * height. In this problem, we are given the base as 21 inches and the height as 12 inches. We need to find the expression that correctly calculates the area.
Applying the formula Substitute the given values into the formula: Area = (1/2) * 21 * 12. This can be rewritten as Area = (21 * 12) / 2.
Comparing with the options Now, let's compare this expression with the given options:
( 21 + 12 ) ÷ 2 - This is incorrect because it adds the base and height instead of multiplying them. ( 21 × 12 ) × 2 - This is incorrect because it multiplies the product of the base and height by 2 instead of dividing by 2. ( 21 × 12 ) ÷ 2 - This is the correct expression as it multiplies the base and height and then divides by 2. ( 21 + 12 ) × 2 - This is incorrect because it adds the base and height and then multiplies by 2.
Final Answer Therefore, the correct expression to calculate the area of the triangle is ( 21 × 12 ) ÷ 2 .
Examples
Understanding how to calculate the area of a triangle is very useful in many real-world situations. For example, if you are designing a triangular garden, you need to calculate its area to determine how much soil to buy. Similarly, architects and engineers use this formula to calculate the area of triangular surfaces in buildings and structures. Knowing the area helps in estimating material costs and ensuring structural stability. Imagine you're tiling a floor with triangular tiles; calculating the area of each tile helps you determine how many tiles you'll need to cover the entire floor. This simple formula is a fundamental tool in various fields.
The area of the triangle can be calculated using the formula Area = 2 1 × base × height . By substituting the values, the correct expression is ( 21 × 12 ) ÷ 2 . So the answer is ( 21 × 12 ) ÷ 2 .
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