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?
$(21+12) \div 2$
$(21+12) \times 2$
$(21 \times 12) \times 2$
$(21 \times 12) \div 2$
Answer (1)
The area of a triangle is calculated using the formula: 2 1 × ba se × h e i g h t .
Substitute the given base (21 inches) and height (12 inches) into the formula.
The expression becomes: 2 1 × 21 × 12 , which is equivalent to ( 21 × 12 ) ÷ 2 .
The correct expression for the area of the triangle is: ( 21 × 12 ) ÷ 2 .
Explanation
Understanding the problem The problem provides the base and height of a triangle and asks for the correct expression to calculate its area. We know that the area of a triangle is given by the formula:
Area formula Area of a triangle = 2 1 × ba se × h e i g h t . In this case, the base is 21 inches and the height is 12 inches.
Substituting values Substituting the given values into the formula, we get: Area = 2 1 × 21 × 12 . This can be rewritten as Area = ( 21 × 12 ) ÷ 2 .
Finding the correct expression Comparing this expression with the given options, we find that the correct expression is ( 21 × 12 ) ÷ 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 useful in many real-world scenarios. For example, if you are designing a triangular garden bed, you need to calculate its area to determine how much soil to buy. Similarly, architects and engineers use triangle area calculations when designing structures, bridges, and other constructions to ensure stability and proper material usage. Knowing this formula helps in efficient planning and resource management in various practical applications.
