iv. 3 cm 4 cm Fig. 1d
The Correct Answer and Explanation is:
The correct answer for the area of the triangle is 6 square centimeters (6 cm²).
Explanation:
The image provided shows a right-angled triangle. We can identify it as a right-angled triangle because of the small square symbol at the vertex where the two sides with lengths 3 cm and 4 cm meet. This symbol indicates that the angle between these two sides is exactly 90 degrees.
To find the area of any triangle, the standard formula is:
Area = ½ × base × height
In a right-angled triangle, the two sides that form the right angle are perpendicular to each other. This convenient property means we can directly use the lengths of these two sides as the base and the height for our area calculation. It does not matter which one you choose as the base and which as the height; the result will be the same.
Let’s assign the values from the figure to the formula:
- Base = 4 cm
- Height = 3 cm
Now, we can substitute these values into the area formula:
Area = ½ × 4 cm × 3 cm
We can perform the calculation in a couple of steps. First, multiply the base and the height together:
4 cm × 3 cm = 12 cm²
Next, we take half of this value, as required by the formula:
Area = ½ × 12 cm²
Area = 6 cm²
The unit for the area is square centimeters (cm²) because we are multiplying two lengths measured in centimeters. This unit represents the amount of two-dimensional space the triangle occupies. Therefore, by applying the fundamental formula for the area of a triangle to the given dimensions, we determine that the area of the figure is 6 square centimeters.
