Question

what is the area?
write your answer as a fraction or as a whole or mixed number.
$1\frac{2}{5}$ yd
$\frac{3}{4}$ yd
\boxed{} square yards
submit

Explanation:

Step1: Recall triangle area formula

The area of a right triangle is $A = \frac{1}{2} \times base \times height$. Here, base is $\frac{3}{4}$ yd and height is $1\frac{2}{5}$ yd.

Step2: Convert mixed number to improper fraction

$1\frac{2}{5} = \frac{1\times5 + 2}{5} = \frac{7}{5}$ yd.

Step3: Substitute into formula

$A = \frac{1}{2} \times \frac{3}{4} \times \frac{7}{5}$. Multiply numerators: $1\times3\times7 = 21$. Multiply denominators: $2\times4\times5 = 40$. So $A = \frac{21}{40}$? Wait, no, wait: $\frac{1}{2} \times \frac{3}{4} \times \frac{7}{5} = \frac{1\times3\times7}{2\times4\times5} = \frac{21}{40}$? Wait, no, wait, height is $1\frac{2}{5} = \frac{7}{5}$, base is $\frac{3}{4}$. So $\frac{1}{2} \times \frac{3}{4} \times \frac{7}{5} = \frac{21}{40}$? Wait, no, let's recalculate: $\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$, then $\frac{3}{8} \times \frac{7}{5} = \frac{21}{40}$. Wait, but let's check again. Wait, $1\frac{2}{5}$ is $\frac{7}{5}$, correct. Base is $\frac{3}{4}$. So area is $\frac{1}{2} \times \frac{3}{4} \times \frac{7}{5} = \frac{21}{40}$? Wait, no, maybe I made a mistake. Wait, $\frac{1}{2} \times \frac{3}{4} = \frac{3}{8}$, then $\frac{3}{8} \times \frac{7}{5} = \frac{21}{40}$. Yes, that's correct. Wait, but let's check the steps again.

Wait, step 1: formula is correct. Step 2: converting $1\frac{2}{5}$ to $\frac{7}{5}$ is correct. Step 3: multiplying $\frac{1}{2} \times \frac{3}{4} \times \frac{7}{5}$. So numerators: 137=21, denominators: 245=40. So area is $\frac{21}{40}$ square yards? Wait, but let's check with decimals. $1\frac{2}{5} = 1.4$, $\frac{3}{4} = 0.75$. Then area is 0.5 0.75 1.4 = 0.5 * 1.05 = 0.525. $\frac{21}{40} = 0.525$, which matches. So that's correct.

Wait, but let me re-express the steps clearly:

Step1: Identify formula

For a right triangle, Area $A = \frac{1}{2} \times b \times h$, where $b$ is base and $h$ is height. Here, $b = \frac{3}{4}$ yd, $h = 1\frac{2}{5}$ yd.

Step2: Convert mixed number to improper fraction

$1\frac{2}{5} = \frac{5\times1 + 2}{5} = \frac{7}{5}$ yd.

Step3: Substitute values into formula

$A = \frac{1}{2} \times \frac{3}{4} \times \frac{7}{5}$

Step4: Multiply the fractions

Multiply the numerators: $1 \times 3 \times 7 = 21$

Multiply the denominators: $2 \times 4 \times 5 = 40$

So, $A = \frac{21}{40}$ square yards.

Answer:

$\frac{21}{40}$