Question

the following diagram shows two triangles. the green (upper) triangle has an area of. the purple (lower) triangle has an area of.

Explanation:

Step1: Recall triangle - area formula

The area formula of a triangle is $A=\frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Step2: Find base and height of green triangle

For the green triangle, by counting the grid - squares, the base $b = 4$ inches and the height $h=3$ inches.

Step3: Calculate area of green triangle

Substitute $b = 4$ and $h = 3$ into the formula: $A_{green}=\frac{1}{2}\times4\times3=6$ square inches.

Step4: Find base and height of purple triangle

For the purple triangle, by counting the grid - squares, the base $b = 4$ inches and the height $h = 3$ inches.

Step5: Calculate area of purple triangle

Substitute $b = 4$ and $h = 3$ into the formula: $A_{purple}=\frac{1}{2}\times4\times3 = 6$ square inches.

Answer:

The green (upper) triangle has an area of 6 square inches. The purple (lower) triangle has an area of 6 square inches.