Question

directions: find the perimeter and area of each figure below. 22. rectangle with side labels (5a^2b^4) and (3ab^2), and some handwritten notes including multiplication and area calculation (a = 15a^3b^6) etc.

Explanation:

Step1: Define rectangle sides

Let length $l = 5a^2b^4$, width $w = 3ab^2$

Step2: Calculate perimeter (sum of sides)

Perimeter $P = 2l + 2w = 2(5a^2b^4) + 2(3ab^2)$
$P = 10a^2b^4 + 6ab^2$

Step3: Calculate area (product of sides)

Area $A = l \times w = (5a^2b^4)(3ab^2)$
Multiply coefficients: $5 \times 3 = 15$
Multiply $a$-terms: $a^2 \times a = a^{2+1} = a^3$
Multiply $b$-terms: $b^4 \times b^2 = b^{4+2} = b^6$
$A = 15a^3b^6$

Answer:

Perimeter: $10a^2b^4 + 6ab^2$
Area: $15a^3b^6$