Find the area of a triangle with base of 10 inches and altitude to the base of 16 inches. 80 in² 135 in² 160 in²
The Correct Answer and Explanation is:
To find the area of a triangle, we use the formula:
[
\text{Area} = \frac{1}{2} \times \text{Base} \times \text{Height}
]
Where:
- The base of the triangle is given as 10 inches.
- The height (altitude) to the base is given as 16 inches.
Step-by-step Calculation:
- Substitute the values into the formula:
[
\text{Area} = \frac{1}{2} \times 10 \, \text{inches} \times 16 \, \text{inches}
]
- Multiply the base and height:
[
10 \times 16 = 160
]
- Now, multiply by ( \frac{1}{2} ) to find the area:
[
\text{Area} = \frac{1}{2} \times 160 = 80 \, \text{inches}^2
]
Thus, the area of the triangle is 80 square inches.
Explanation:
The formula for the area of a triangle is derived from the fact that a triangle is essentially half of a rectangle with the same base and height. In a rectangle, the area is calculated as:
[
\text{Area of rectangle} = \text{Base} \times \text{Height}
]
Since a triangle only takes up half of the space compared to the corresponding rectangle, we divide the product of the base and height by 2. In this case, you were given the dimensions of the base (10 inches) and height (16 inches), so we simply multiplied these together and then divided by 2 to get the final area of 80 square inches.
Thus, the correct answer is 80 in².
Final Answer:
The area of the triangle is 80 square inches.