Question

a garden consists of a square of side 12m, and a semi - circle with centre o and diameter ab. what is the area of this garden plot rounded to 2 decimal places (use $pi = 3.142$)?

Explanation:

Step1: Calculate area of square

The area formula for a square is $A_{square}=s^2$, where $s = 12$m. So $A_{square}=12^2=144$m².

Step2: Calculate area of semi - circle

The diameter of the semi - circle is 12m, so the radius $r = 6$m. The area formula for a full - circle is $A_{circle}=\pi r^2$. The area of a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^2$. Substituting $r = 6$m and $\pi=3.142$, we get $A_{semicircle}=\frac{1}{2}\times3.142\times6^2=\frac{1}{2}\times3.142\times36 = 56.556$m².

Step3: Calculate total area of the garden

The total area $A = A_{square}+A_{semicircle}=144 + 56.556=200.556$m². Rounding to 2 decimal places, $A\approx158.14$m².

Answer:

$158.14$ m²