Question

A triangular road sign has a height of 3 feet and a base of 2.5 feet. How much larger in area is this sign than one with a height of 2.5 feet and a base of 3 feet?

Answer 1

Not larger or smaller; the areas are the same

Explanation:

Recall that the formula for the area of a triangle of base b and height h is

A = (1/2)(b)(h).

In the first case, h = 3 ft and b = 2.5 ft. This results in an area of 3.75 ft^2.

In the second case, h = 2.5 ft and b = 3 ft. The area is the same: 3.75 ft^2.

This is because A = (1/2)(b)(h) has the same value regardless of the order in which b and h are used as multipliers.

There is no difference in the areas of the two signs. The areas are the same.