Answer:
Area of Diagram 1 = 72 unit²
Area of Diagram 2 = 190 unit²
Area of Diagram 3 = 36 unit²
Step-by-step explanation:
In each of the diagrams shown, there are triangles and rectangles.
Note that: Area of Triangle = 1/2(Base x Height)
Area of Rectangle = Length x Breath
<u>Area of Diagram 1 </u>
= Area of Triangle 1 (+) Area of Rectangle (+) Area of Triangle 2.
<em>Triangle 1</em>: height = 6 units , base = 3 units
∴ Area = 1/2 * (6 units x 3 units) ==> 1/2 * (18 unit²) ==> 9 unit²
<em>Rectangle</em>: Length = 9 units , Breadth = 6 units
∴ Area = 9 units x 6 units = 54 unit²
<em>Triangle 2</em>: height = 6 units , base = 3 units
∴ Area = 1/2 * (6 units x 3 units) ==> 1/2 * (18 unit²) ==> 9 unit²
Recall; Area of Triangle 1 (+) Area of Rectangle (+) Area of Triangle 2 = Area of Diagram.
∴ Area of Diagram 1 = 9 unit² + 54 unit² + 9 unit² = <u>72 unit²</u>
<u>Area of Diagram 2 </u>
= Area of Triangle 1 (+) Area of Rectangle (+) Area of Triangle 2.
<em>Triangle 1</em>: height = 10 units , base = 3 units
∴ Area = 1/2 * (10 units x 3 units) ==> 1/2 * (30 unit²) ==> 15 unit²
<em>Rectangle</em>: Length = 15 units , Breadth = 10 units
∴ Area = 15 units x 10 units = 150 unit²
<em>Triangle 2</em>: height = 10 units , base = 5 units
∴ Area = 1/2 * (10 units x 5 units) ==> 1/2 * (50 unit²) ==> 25 unit²
Recall; Area of Triangle 1 (+) Area of Rectangle (+) Area of Triangle 2 = Area of Diagram.
∴ Area of Diagram 2 = 15 unit² + 150 unit² + 25 unit² = <u>190 unit²</u>
<u></u>
<u>Area of Diagram 3 </u>
= Area of Triangle 1 (+) Area of Triangle 2 (+) Area of Rectangle.
<em>Triangle 1</em>: height = 4 units , base = 4 units
∴ Area = 1/2 * (4 units x 4 units) ==> 1/2 * (16 unit²) ==> 8 unit²
<em>Triangle 2</em>: height = 4 units , base = 2 units
∴ Area = 1/2 * (4 units x 2 units) ==> 1/2 * (8 unit²) ==> 4 unit²
<em>Rectangle</em>: Length = (8 - 2) units = 6 units, Breadth = 4 units
∴ Area = 6 units x 4 units = 24 unit²
Recall; Area of Triangle 1 (+) Area of Triangle 2 (+) Area of Rectangle = Area of Diagram.
∴ Area of Diagram 3 = 8 unit² + 4 unit² + 24 unit² = <u>36 unit²</u>
