Question

directions: find the perimeter and area of each figure below.
22.
23.

1. (assume the triangle below is equilateral.)

directions: find the area of each figure below.
25.
26.

Explanation:

22. Step1: Calculate rectangle perimeter

Perimeter = $2\times(length + width)$
$P = 2(5a^2b^4 + 3ab^2)$
$P = 10a^2b^4 + 6ab^2$

22. Step2: Calculate rectangle area

Area = $length \times width$
$A = 5a^2b^4 \times 3ab^2$
$A = 15a^3b^6$

23. Step1: Calculate triangle perimeter

Perimeter = sum of all sides
$P = 4m^2 + 3mn^2 + 7mn^2$
$P = 4m^2 + 10mn^2$

23. Step2: Calculate right triangle area

Area = $\frac{1}{2} \times leg_1 \times leg_2$
$A = \frac{1}{2} \times 4m^2 \times 3mn^2$
$A = 6m^3n^2$

24. Step1: Calculate equilateral triangle perimeter

First, find side length using area formula $A=\frac{1}{2}\times base \times height$, solve for side (base = side = $s$):
$A=\frac{1}{2} \times 8mn \times 4m^2 = 16m^3n$, then confirm side $s=8mn$
Perimeter = $3 \times side$
$P = 3 \times 8mn$
$P = 24mn$

24. Step2: Calculate equilateral triangle area

Area = $\frac{1}{2} \times base \times height$
$A = \frac{1}{2} \times 8mn \times 4m^2$
$A = 16m^3n$

25. Step1: Calculate trapezoid area

Area = $\frac{1}{2} \times (top + bottom) \times height$
$A = \frac{1}{2}(7a^2b + 11a^2b) \times 3ab$
$A = \frac{1}{2}(18a^2b) \times 3ab$
$A = 9a^2b \times 3ab$
$A = 27a^3b^2$

26. Step1: Calculate circle area

Area = $\pi \times radius^2$
$A = \pi(3x^2y)^2$
$A = 9\pi x^4y^2$

Answer:

1. Perimeter: $10a^2b^4 + 6ab^2$, Area: $15a^3b^6$
2. Perimeter: $4m^2 + 10mn^2$, Area: $6m^3n^2$
3. Perimeter: $24mn$, Area: $16m^3n$
4. Area: $27a^3b^2$
5. Area: $9\pi x^4y^2$