Question

find the area of the following polygon given in the first column
a. a square with side 6 cm (with right angles marked)
b. a parallelogram with base 10 in and height 4 in (dotted height line)
c. a trapezoid with top base 2 ft, bottom base 12 ft, and height 10 ft (dotted height line)
d. a triangle with base 8 m and height 3 m (dotted height line)

Explanation:

Step1: Calculate area of square

The shape is a square with side length $6\ \text{cm}$. Area formula: $A = s^2$
$A_a = 6^2 = 36\ \text{cm}^2$

Step2: Calculate area of parallelogram

Use base $10\ \text{in}$ and height $4\ \text{in}$. Area formula: $A = b \times h$
$A_b = 10 \times 4 = 40\ \text{in}^2$

Step3: Calculate area of trapezoid

Use bases $2\ \text{ft}$, $12\ \text{ft}$, height $10\ \text{ft}$. Area formula: $A = \frac{1}{2}(b_1+b_2)h$
$A_c = \frac{1}{2}(2+12) \times 10 = 70\ \text{ft}^2$

Step4: Calculate area of triangle

Use base $9\ \text{m}$ and height $3\ \text{m}$. Area formula: $A = \frac{1}{2}bh$
$A_d = \frac{1}{2} \times 9 \times 3 = 13.5\ \text{m}^2$

Answer:

a. $36\ \text{cm}^2$
b. $40\ \text{in}^2$
c. $70\ \text{ft}^2$
d. $13.5\ \text{m}^2$