A house shaped like an octagon has a large porch, as shown.
What's the area of the house and porch?
Answers
Answer:
1175
Step-by-step explanation:
To find the area, first find the area of the rectangle formed by the porch and most of the house.
A=l×b
A = (10+15)×30
=35×30
=1050
Then, find the area of the trapezium at the top of the house.
A=0.5(a+b)h
=0.5(30+20)×5
=125.
Lastly, add both areas.
1050+125=1175
Given:
The shape of the house is an octagon.
To find:
The area of the house and porch
Solution:
The area of the house is 550 feet² and the porch is 325 feet².
We can find the area by following the given steps-
We know that the area of the house is equal to the area of a rectangle and two trapeziums.
The length of the rectangular area=30 feet
The width of the rectangular area=10 feet
The height of the trapezium=5 feet
The length of the shorter parallel side of the trapezium= 30-10=20 feet
The length of the longer parallel side of the trapezium=30 feet
The area of the house= The area of the rectangular region+ area of two trapeziums
The area of the rectangular region= Length× width
=30×10=300 feet²
The area of a trapezium= 1/2× height× (sum of parallel sides)
=1/2×5×(20+30)
=1/2×5×50=125 feet²
The area of two trapeziums= 2× 125=250 feet²
On putting the values,
The area of the house= 300+250=550 feet²
Now, the area of the porch = Area of the rectangular porch area-area of a trapezium
Area of the rectangular porch=length of porch ×width of the porch
=30×15
=450 feet²
Area of the porch= 450-125=325 feet²
Therefore, the area of the house is 550 feet² and the porch is 325 feet².