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You need to find the length of A F and BC first
Lets call BC --> 'x'
Lets form an equation
9 + 9 + x + x = 28
18 + 2x = 28
- 18
2x = 10
/ 2
x = 5
So now we have the length BC
We can subtract this length from the 11cm to find the vertical height of the trapezium
11 - 5 = 6
Now we have all we need to work it out.
area = (a + b) / 2 x h
area = (5 + 9) / 2 x 6
area = 42 cm^2
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Answer:
42 cm²
Step-by-step explanation:
We can see this shape is made of 2 shapes that we are familiar with which are a rectangle and a trapezium.
⇒ The first step in working out the area of the trapezium is working out the length of CB and then working out the height of trapezium. We are given that the perimeter of the rectangle is 28 cm and we know that opposite sides of a rectangle are equal so we will call the length we want to work out x
→ x + x + 9 + 9 = 28
⇒ Simplify
→ 2x + 18 = 28
⇒ Minus 18 from both sides to isolate 2x
→ 2x = 10
⇒ Divide both sides by 5 to isolate x
→ x = 5
5 cm is the length of CB, we will need to minus that from 11 to find the height of the trapezium so,
11 - 5 = 6. The height of the trapezium is 6
Now we have the height of the trapezium (6), we have the base (9) and we have the top length (5). All we do now is substitute these numbers into the trapezium formula which is
→ 0.5 × ( a + b ) × h
Where 'a' and 'b' are the parallel sides and 'h' is the height
Now we begin to substitute in the values,
→ 0.5 × ( a + b ) × h
⇒ Substitute in the values
→ 0.5 × ( 5 + 9 ) × 6
⇒ Simplify
→ 0.5 × ( 14 ) × 6
⇒ Simplify further
→ 42
The area of the trapezium is 42 cm²
