Question

calculating areas of multiple polygons
each unit on the coordinate grid represents 1 yard. the rectangular pool and triangular hot tub shown are both in need of covers. how much total material is needed to cover both? square yards

Explanation:

Step1: Find area of rectangle

Use formula \(A = l\times w\). By counting grid - units, length \(l = 5\) yards and width \(w = 4\) yards. So \(A_{rectangle}=5\times4 = 20\) square yards.

Step2: Find area of triangle

Use formula \(A=\frac{1}{2}bh\). By counting grid - units, base \(b = 2\) yards and height \(h = 2\) yards. So \(A_{triangle}=\frac{1}{2}\times2\times2= 2\) square yards.

Step3: Find total area

Add the area of the rectangle and the area of the triangle. \(A_{total}=A_{rectangle}+A_{triangle}=20 + 2=22\) square yards.

Answer:

22