Answer:
Step-by-step explanation:
Arrays are useful representations of multiplication concepts of the commutative property.
We need to find how can you use an array to show the commutative property.
The word 'commutative' originates from the word 'commute', which means to move around. Hence, the commutative property deals with moving the numbers around. So mathematically, if changing the order of the operands does not change the result of the arithmetic operation then that particular arithmetic operation is commutative.
An arrangement of objects, pictures, or numbers in rows and columns is called an array. Arrays are useful representations of multiplicationconcepts (among other ideas in mathematics).
The commutative property of multiplication can be neatly illustrated using an array. For example, the array above could be read as 2 rows of 6, or as 6 columns of 2. Or the array could be physically turned around to show that 2 rows of 6 have the same number as 6 rows of 2.
Therefore, arrays are useful representations of multiplication concepts of the commutative property.
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Find the area of each figure. Round to the nearest tenth if
necessary.
(Example
(02 cm
12 cm
6 yd
4.5 cm
16 yd
8 yd
2 cm
show) 24 yd
5 cm
1 m.
15 c
15 m
Answer:
1. 64 cm²
2. 240 yard²
3. 85.13 cm²
4. 193.36 m²
Step-by-step explanation:
Ques 1: We are given two rectangle with dimensions,
Length = 12 cm, Width = 4.5 cm and Length = 5 cm, Width = 2 cm.
As, we know, Area of a rectangle = Length × Width
So, we have,
Area of 1st rectangle = 12 × 4.5 = 54 cm²
Area of 2nd rectangle = 5 × 2 = 10 cm²
Thus, the total area of the figure = 54 + 10 = 64 cm²
Ques 2: We are given a triangle and a rectangle with dimensions,
Triangle: Base = 24-12 = 12 yd and Height = 8 yd
As, Area of a triangle =
i.e. Area of the triangle =
i.e. Area of the triangle =
i.e. Area of the triangle = 48 yard²
Rectangle: Length = 24 yd, Width = 8 yd
As, we know, Area of a rectangle = Length × Width
i.e. Area of a rectangle = 24 × 8 = 192 yard²
So, the total area of the figure = 48 + 192 = 240 yard².
Ques 3: We are given a triangle and a semi-circle with dimensions,
Triangle: Base = 8 cm and Height = 15 cm
As, Area of a triangle =
i.e. Area of the triangle =
i.e. Area of the triangle =
i.e. Area of the triangle = 60 cm²
Semi-circle: Diameter = 8 cm implies Radius = 4 cm.
So, Area of the semi-circle =
i.e. Area of the semi-circle =
i.e. Area of the semi-circle =
i.e. Area of the semi-circle =
i.e. Area of the semi-circle = 25.13 cm²
Thus, the total area of the figure = 60 + 25.13 = 85.13 cm²
Ques 4: We are given a rectangle and a semi-circle of dimensions,
Rectangle: Length = 15 m, Width = 7 m.
As, we know, Area of a rectangle = Length × Width
i.e. Area of a rectangle = 15 × 7 = 105 m²
Semi-circle: Diameter = 15 m implies Radius = = 7.5 m
So, Area of the semi-circle =
i.e. Area of the semi-circle =
i.e. Area of the semi-circle =
i.e. Area of the semi-circle = 88.36 m²
Thus, the total area of the figure = 105 + 88.36 = 193.36 m²