Question

2 for each triangle, a base and its corresponding height are labeled. a. find the area of each triangle. b. how is the area related to the base and its corresponding height?

Explanation:

Step1: Recall area formula

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

Step2: Calculate area of triangle A

For triangle A, $b = 4$ and $h=6$. Substitute into the formula: $A_A=\frac{1}{2}\times4\times6 = 12$.

Step3: Calculate area of triangle B

For triangle B, $b = 8$ and $h = 4$. Substitute into the formula: $A_B=\frac{1}{2}\times8\times4=16$.

Step4: Calculate area of triangle C

For triangle C, $b = 8$ and $h = 4$. Substitute into the formula: $A_C=\frac{1}{2}\times8\times4 = 16$.

Step5: Answer part b

The area of a triangle is half the product of its base and the corresponding height, i.e., $A=\frac{1}{2}bh$.

Answer:

a. Triangle A: 12, Triangle B: 16, Triangle C: 16
b. The area of a triangle is half the product of its base and the corresponding height.