Applying the formula for each identified shape that are given, the correct areas to each shape are:
a. <em>Square </em>= 134.6 sq. yd
b. <em>Circle </em>= 452.2 sq. cm
c. <em>Parallelogram </em>= 40.6 sq. cm
d. <em>Rectangle </em>= 43.2 sq. ft
e. <em>Trapezium </em>= 25.7 sq. m
f. <em>Triangle</em> = 21.6 sq. ft
a. The shape given is a square.
Area of the square = ![s^2](https://tex.z-dn.net/?f=s%5E2)
Where,
s = 11.6 yd
Plug in the value of s
Area of the square = ![11.6^2 = 134.6 $ yd^2](https://tex.z-dn.net/?f=11.6%5E2%20%3D%20134.6%20%24%20yd%5E2)
b. The shape given is a circle.
Area of the circle = ![\pi r^2](https://tex.z-dn.net/?f=%5Cpi%20r%5E2)
r = 12 cm
Area of the square = ![\pi \times 12^2 = 452.2 $ cm^2](https://tex.z-dn.net/?f=%5Cpi%20%5Ctimes%2012%5E2%20%3D%20452.2%20%24%20cm%5E2)
c. The shape given is a parallelogram.
Area of the parallelogram = ![bh](https://tex.z-dn.net/?f=bh)
b = 7 cm
h = 5.8 cm
- Plug in the value of b and h
Area of the parallelogram = ![7 \times 5.8 = 40.6 $ cm^2](https://tex.z-dn.net/?f=7%20%5Ctimes%205.8%20%3D%2040.6%20%24%20cm%5E2)
d. The shape given is a rectangle.
Area of the rectangle = ![l \times w](https://tex.z-dn.net/?f=l%20%5Ctimes%20w)
l = 8.3 ft
w = 5.2 ft
- Plug in the value of l and w
Area of the rectangle = ![8.3 \times 5.2 = 43.2 $ ft^2](https://tex.z-dn.net/?f=8.3%20%5Ctimes%205.2%20%3D%2043.2%20%24%20ft%5E2)
e. The shape given is a trapezium.
Area of the trapezium = ![\frac{1}{2} (a + b) \times h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%28a%20%2B%20b%29%20%20%5Ctimes%20h)
a = 2.8 m
b = 10.4 m
h = 3.9 m
- Plug in the value of a, b, and h
Area of the trapezium = ![\frac{1}{2}(2.8 + 10.4) \times 3.9 = 25.7 $ m^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%282.8%20%2B%2010.4%29%20%5Ctimes%203.9%20%3D%2025.7%20%24%20m%5E2)
f. The shape given is a triangle. <em>(See attachment for the shape).</em>
Area of the triangle = ![\frac{1}{2} \times b \times h](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%20%5Ctimes%20b%20%20%5Ctimes%20h)
b = 9 ft
h = 4.8 ft
- Plug in the value of b, and h
Area of the triangle = ![\frac{1}{2} \times 9 \times 4.8 = 21.6 $ ft^2](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%20%5Ctimes%209%20%5Ctimes%204.8%20%3D%2021.6%20%24%20ft%5E2)
Therefore, applying the formula for each identified shape that are given, the correct areas to each shape are:
a. <em>Square </em>= 134.6 sq. yd
b. <em>Circle </em>= 452.2 sq. cm
c. <em>Parallelogram </em>= 40.6 sq. cm
d. <em>Rectangle </em>= 43.2 sq. ft
e. <em>Trapezium </em>= 25.7 sq. m
f. <em>Triangle</em> = 21.6 sq. ft
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