Question

the equation $a = \frac{1}{2}(b_1 + b_2)h$ can be used to determine the area, $a$, of a trapezoid with height, $h$, and base lengths, $b_1$ and $b_2$. which are equivalent equations? check all that apply.$\frac{2a}{h}-b_2 = b_1LXB0\frac{2a - b_2}{h}= b_1LXB1\frac{a}{2(b_1 + b_2)}= h$

Explanation:

Step1: Start with original formula

$$a = \frac{1}{2}(b_1 + b_2)h$$

Step2: Eliminate the fraction

Multiply both sides by 2:
$$2a = (b_1 + b_2)h$$

Step3: Solve for $b_1$

Divide by $h$, then subtract $b_2$:
$$\frac{2a}{h} = b_1 + b_2$$
$$\frac{2a}{h} - b_2 = b_1$$

Step4: Solve for $h$

Divide both sides of $2a=(b_1+b_2)h$ by $(b_1 + b_2)$:
$$\frac{2a}{b_1 + b_2} = h$$

Step5: Verify other options

Check remaining options:

• $\frac{a}{2h}-b_2=b_1$: Fails (incorrect division step)
• $\frac{2a - b_2}{h}=b_1$: Fails (incorrect distribution)
• $\frac{a}{2(b_1 + b_2)}=h$: Fails (incorrect division step)

Answer:

$\frac{2a}{h}-b_2 = b_1$
$\frac{2a}{b_1 + b_2} = h$