Compound Shapes: How to Find the Area of an L-Shape
Area Of A Composite Shape Video
A compound shape is a shape that is made up from other simple shapes. In this article we will be working out the area of a L shape (made up from 2 rectangles). To find the area of a compound shape, follow these simple steps:
Step 1: Work out the missing lengths around the edge of the compound shape.
Step 2: Divide your L shape into two rectangles. This can be done in 2 different ways (both methods will give the same answer).
Step 3: Work out the area of each rectangle. Do this by multiplying the base of the rectangle by the height of the rectangle.
Step 4: Add the areas of the rectangles together to give the total area of the L shape.
Example 1
Find the area of this compound shape (L shape).
Step 1
Work out the missing lengths around the edge of the compound shape.
10 – 6 = 4 cm
9 – 2 = 7 cm
Step 2
Divide your L shape into two rectangles.
In this case I have put the line horizontal.
Read More From Owlcation
Step 3
Now you need to find the area of the 2 rectangles:
The area of rectangle A is 10 × 2 = 20 cm²
The area of rectangle B is 4 × 7 = 28 cm²
Make sure you select the correct base and height lengths for each rectangle.
Step 4
All you need to do now is to add up the 2 answers from step 3.
20 + 28 = 48 cm².
So the total area of the compound shape is 48 cm².
Summary:
Find the missing lengths around your L shape and divide the shape into 2 rectangles. Find the area of both rectangle and add them up to give the total area of the compound shape.
Questions & Answers
Question: How do you know which sides to multiply on the L shape?
Answer: It must be the length and width of the rectangle (these are the two side lengths which make the rectangle).
Question: How do you find the area of a frame?
Answer: Work out the area of the inner and outer rectangles, and then find the difference between these area.
Assuming that the frame is rectangular.
Question: How do you know you have to put the line horizontal not vertical when finding the area of an L-shape?
Answer: You can split the compound shape up either way.
Both ways will result in the correct area.
Question: How do I find the perimeter of an L shape?
Answer: Once you have worked out all of the sides lengths, then you can add all these up to give the perimeter of the L shape.
Question: How do you work out the volume of a prism from calculating the area of an L shape?
Answer: Once you have calculated the cross-sectional area of the prism, multiply the answer by the length of the prism.
So for example, if the cross-sectional area of the L shape was 50 cm^2 and the length 3cm, then the volume of the L shape would be 150 cm^3 (50 multiplied by 3).
Question: How do you know where to draw the line in order to have two rectangles?
Answer: It can be horizontal or vertical, as long as it makes two rectangles.
Question: How do you know which measurements you are meant to multiply to find the area of a complex shape?
Answer: You multiply the two side lengths of each rectangle together (Base multiplied by Height).
Question: What if I need to find the area of something that is not L-shaped?
Answer: Other shapes can be split into rectangles too. T and H shapes are also common exam questions.
Question: How do you know which numbers to add and which numbers to subtract when finding the area of an L-shape?
Answer: If the length your finding is longer than the two other sides then add them, if not subtract them.
Question: Is it only an L shape that can be used for compound shape?
Answer: No, it can be other shapes too, such as a T shape, or a H shape.
Question: How do you calculate perimeter?
Answer: The perimeter can be found by adding up all the side lengths around the L shape.
Question: How do you find the area if the shape has a half circle conected to it?
Answer: I think you mean a shape which can be split into a rectangle (or square) and a semi-circle.
Work out the area of the rectangle using length times width, and work out the area of the semi-circle using 0.5 times Pi times radius squared. Then add these two answers together.
Question: What does finding the area of the smaller shapes of an L shape help with?
Answer: Area helps you work out the space inside a shape.
It can be useful in real life for working out how much carpet you need to fit a floor space, or how much gravel you need to fill a garden.
Comments
Adnan Alam on June 16, 2018:
thank you so much!! i appreciate!!!! luv u!!!!
vee on July 16, 2013:
thnx i got it nw
matt on July 05, 2013:
anyone know how calculate a 2 cm border around this?
Will the master of chess on June 19, 2013:
the teacher was not as good as this
hameed khan on June 06, 2013:
Good Process but long Process....
man on May 02, 2013:
Cheers mate really helped
New new on April 23, 2013:
Thxx but I already knew how to do it I just need to see if I was rite but u did hlp with it so thx for dat bye
isabella on January 14, 2013:
THAN YOU!!!!!!!!!!!!!!!!!!!!!!!!!! Now I remember!!
shruti jain on June 06, 2012:
thank u but i didn't get the perimeter of L !! so if someone knows it plzz tell!!!
x.x.x.Tabz.x.x.x on June 05, 2012:
thx dat was a lot of help!!!
Princess Libyan on April 23, 2012:
Thanks God I've done this homework good with this help!!!
Thanks lots!! ;)
khaay on April 19, 2012:
Thamks a lot for your help ! ! doing my aims and i didn't know how to do this but now i do because of you ! : )
jessics on April 17, 2012:
thank you!!!
danny on March 27, 2012:
lots of help thanks :)
BROWNGURL on March 05, 2012:
thes help a lot in my homework hu ever did thes web thakes a lot
adan on February 02, 2012:
awsum dude i appreciate it
margaret on January 31, 2012:
u r the beep in the whole universe
ninja girl on January 02, 2012:
very helpful
hmmm on December 28, 2011:
thanks i got 11 plus so that help's
queen on November 25, 2011:
thx for help did th job
princess on November 21, 2011:
lots of help for me !!!!!!!
miss bossy on November 15, 2011:
this is very good help i think
gogoluvr224 on April 04, 2011:
plenty help!
guy 1000 in a million on February 06, 2011:
lots of help
kool person on August 30, 2010:
YAY!!!!!!! LoTs Of HeLp!
cool on August 28, 2010:
good
sean on May 19, 2010:
wonderful thank u for the help
