Question

two triangles labeled a (top) and b (bottom) on a square grid, with black vertices and shaded interiors. triangle a has a vertical side, horizontal top, and diagonal hypotenuse. triangle b has a vertical side, horizontal bottom, and diagonal hypotenuse.

Explanation:

To determine the relationship between the areas of triangles A and B, we can use the formula for the area of a triangle, \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).

Step 1: Analyze Triangle A

• Let's assume each grid square has a side length of 1 unit.
• For Triangle A:
• The base (horizontal side) spans 4 units (from the leftmost to the rightmost point horizontally).
• The height (vertical side) spans 3 units (from the bottom to the top point vertically).
• Using the area formula: \( \text{Area of A} = \frac{1}{2} \times 4 \times 3 \)
• Calculate: \( \frac{1}{2} \times 4 \times 3 = 6 \) square units.

Step 2: Analyze Triangle B

• For Triangle B:
• The base (horizontal side) spans 4 units (from the leftmost to the rightmost point horizontally).
• The height (vertical side) spans 3 units (from the bottom to the top point vertically).
• Using the area formula: \( \text{Area of B} = \frac{1}{2} \times 4 \times 3 \)
• Calculate: \( \frac{1}{2} \times 4 \times 3 = 6 \) square units.

Answer:

The areas of Triangle A and Triangle B are equal (both have an area of 6 square units).