Answer is Provided in the image attached.
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1 answer:
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To solve this problem, we need to first find the dimensions of the side of the blue and purple squares.
We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.
The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.
Therefore
Area of band
[recall 
or 20(x+5) if you wish.
We're given that the purple (smaller) square has a side length of x inches.
We are also given that the blue band has a width of 5 inches.
Since the blue band surrounds the purple square on both sides, the length of the blue square is x+2(5)=x+10 inches.
The net area of the band is therefore the difference of the area of the blue square and the purple square, namely take out the area of the purple square from the blue.
Therefore
Area of band
Given:
x = 12 in, y = 16 in and z = 20 in
To find:
The surface area of the geometric shape.
Solution:
Area of top rectangle = z × z
= 20 × 20
Area of top rectangle = 400 in²
Area of middle rectangle = z × y
= 20 × 16
Area of middle rectangle = 320 in²
Area of bottom rectangle = z × x
= 20 × 12
Area of bottom rectangle = 240 in²
Area of left triangle =
Area of left triangle = 96 in²
Area of right triangle =
Area of right triangle = 96 in²
Surface area = 400 + 320 + 240 + 96 + 96
= 1152
The surface area of the geometric shape is 1152 in².