Question

a patio area is to be covered with outdoor tile. what is the area of the patio? 24 m 9 m 6 m 18 m 27 m 33 m

Explanation:

Step1: Divide the shape into a triangle, a rectangle and a smaller rectangle

The overall shape can be split into a triangle on the left - hand side, a large rectangle in the middle and a smaller rectangle on the top - right.

Step2: Calculate the area of the triangle

The formula for the area of a triangle is $A_{triangle}=\frac{1}{2}bh$. Here, the base $b = 9$m and the height $h = 6$m. So $A_{triangle}=\frac{1}{2}\times9\times6= 27$m².

Step3: Calculate the area of the large rectangle

The formula for the area of a rectangle is $A_{rectangle}=lw$. The length $l = 33$m and the width $w=18$m. So $A_{rectangle1}=33\times18 = 594$m².

Step4: Calculate the area of the smaller rectangle

The length of the smaller rectangle is $24$m and the width is $27 - 18=9$m. So $A_{rectangle2}=24\times9 = 216$m².

Step5: Calculate the total area of the patio

The total area $A = A_{triangle}+A_{rectangle1}+A_{rectangle2}$. So $A=27 + 594+216=837$m².

Answer:

$837$ m²