Question

find the area.
(the image shows a right triangle with one leg labeled $5y^3x^2$ and the other leg labeled $yx^2$)

Explanation:

Step1: Recall Triangle Area Formula

The area of a right triangle is $\frac{1}{2} \times \text{base} \times \text{height}$. Here, base is $yx^2$ and height is $5y^3x^2$.

Step2: Substitute into Formula

Area $= \frac{1}{2} \times (yx^2) \times (5y^3x^2)$

Step3: Multiply Variables

Multiply coefficients and use exponent rules ($a^m \times a^n = a^{m + n}$):
Coefficients: $\frac{1}{2} \times 5 = \frac{5}{2}$
$x$ terms: $x^2 \times x^2 = x^{2 + 2} = x^4$
$y$ terms: $y \times y^3 = y^{1 + 3} = y^4$

Step4: Combine Results

Area $= \frac{5}{2}x^4y^4$

Answer:

$\frac{5}{2}x^4y^4$