Part 1: getting the area of the entrance The entrance has a trapezoid shape. Area of trapezoid can be calculated using the following rule: Area of trapezoid = average base * height The aveage base = (b1+b2)/2 = (8+16)/2 = 12 ft height of trapezoid = 4 ft Therefore: area of entrance = 12*4 = 48 ft^2
Part 2: getting the area of the house: area of house = area of back porch + area of side deck + area of play room + area of entrance i- getting the area of the back porch: The back porch is a square with side length = 6 ft Therefore: area of back porch = 6*6 = 36 ft^2 ii- getting the area of side deck: The side deck is a rectangle whose length is 14 ft and width is 3 ft Therefore: area of side deck = 14*3 = 42 ft^2 iii- getting the area of play room: The play room is a rectangle whose length is 14 ft and width is 16 ft Therefore: area of play room = 14*16 = 224 ft^2 iv- area of entrance is calculated in part 1 = 48 ft^2 Based on the above: area of house = 36 + 42 + 224 + 48 = 350 ft^2
This is a geometric series with a common ratio between successive terms that is less than 1 in absolute value. This means the series will converge. The value of the sum is .
