Answer:
1. A = 2x; P = 4x+2. A = 4; P = 10.
2. A = y² +2; P = 4y +2. A = 27; P = 22.
Step-by-step explanation:
1. The area is the sum of the marked areas of each of the tiles:
A = x + x
A = 2x
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The perimeter is the sum of the outside edge dimensions of the tiles. Working clockwise from the upper left corner, the sum of exposed edge lengths is ...
P = 1 + (x-1) + x + 1 + (x+1) + x
P = 4x +2
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When x=2, these values become ...
A = 2·2 = 4 . . . . square units
P = 4·2+2 = 10 . . . . units
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2. Again, the area is the sum of the marked areas:
A = y² + 1 + 1
A = y² +2
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The edge dimension of the square y² tile is presumed to be y, so the perimeter (starting from upper left) is ...
P = y +(y-2) +1 +2 +(y+1) +y
P = 4y +2
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When y=5, these values become ...
A = 5² +2 = 27 . . . . square units
P = 4·5 +2 = 22 . . . . units
<h2>Solution (1) :</h2>
∠<em>y</em><em> </em>and ∠<em>x</em> are alternate interior angles . Both of these angles will be equal in measure when on two parallel lines with a transversal .
<h2>Solution (2) :</h2>
∠y and ∠x are alternate interior angles . Both of these angles will have an equal angle measure when they lie on two parallel lines with a transversal .
<h2>Solution (3) :</h2>
∠y and ∠x vertically opposite angles . Both of these angles will be equal in measure when on two parallel lines with a transversal .
<h2>Solution (4) :</h2>
∠y and ∠x are adjacent angles as well as a linear pair . These angles will sum up to form 180° .
<, > - open circle
≤, ≥ - closed circle
<, ≤ - draw to the left
>, ≥ - draw to the right
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We have x ≥ 3
closed circle on number 3 and draw the line to the right
