Final answer:
To find the area of a triangle when given the area of a rectangle with the same base and height, divide the rectangle's area by two. When comparing areas of squares with different side lengths, the area is proportional to the square of the side length. For instance, a square with sides twice the length of another has four times the area.
Step-by-step explanation:
To find the area of a triangle using the area of a rectangle, you need to know that the triangle is half of a rectangle if they share the same base and height. The formula for the area of a rectangle is base times height, while the formula for the area of a triangle is 1/2 × base × height. Therefore, if you know the area of the rectangle, you can divide it by two to get the area of the triangle.
For example, if the rectangle’s area is given as 200 square units, and the triangle has the same base and height as the rectangle, the triangle's area would be 1/2 × 200, which equals 100 square units.
When comparing areas of different shapes, remember that the relationship is proportional to the square of their linear dimensions. So, if a larger square has side lengths that are twice as long as a smaller square's sides, the area of the larger square will be four times greater because the area is proportional to the side length squared (2×2).
As for the calculation involving measurements, let’s take the triangle with a base of 1.007 m and a height of 0.665 m. The area of this triangle is 1/2 × 1.007 m × 0.665 m, which to three significant figures is approximately 0.335 m².
Applying these principles will allow you to solve problems related to finding areas of triangles and compare areas of different shapes efficiently.