As in the figure below, triangle A and triangle B share a common base, and the height of A is double the height of B. If B has an area of 16, how large is A?
Answer (2)
To find the area of triangle A, let's first understand the relationship between the two triangles.
Common Base: Both triangles A and B share the same base, which means the only difference in their areas is due to their heights.
Height Relationship: The problem states that the height of triangle A is double the height of triangle B.
Area of Triangle B: We know the area of triangle B is given as 16.
The formula for the area of a triangle is:
Area = 2 1 × base × height
Area of Triangle A: Since the height of triangle A is double that of triangle B, the area of triangle A will be double the area of triangle B (because the base is the same and only the height changes).
Therefore, if triangle B has an area of 16, then:
Area of Triangle A = 2 × 16 = 32
So, the area of triangle A is 32 square units.
The area of triangle A is found by recognizing that it shares a base with triangle B and has a height that is twice as long. Given triangle B's area of 16 square units, triangle A's area is calculated to be 32 square units. Thus, the area of triangle A is 32 square units.
;
