A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

The area of a rectangle is equal to its length x width:

a = l x w
a = a x b
a = 1 x 8
a = 8

You need to find the value of a so solve the first equation in terms of x:

-4a + x = -4
x = -4 + 4a

then substitute the result (-4 - -4a) into the second equation:

9a + 9(-4 + 4a) = 7
9a + (9 x -4) + (9 x 4a) = 7
9a - 36 + 36a = 7
9a + 36a = 7 + 36
45a = 43
a = \( \frac{43}{45} \)
a = \(\frac{43}{45}\)

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with a° = 37, the value of d° is 143.

The formula for area is πr². Radius is circle \( \frac{diameter}{2} \):

r = \( \frac{d}{2} \)
r = \( \frac{4}{2} \)
r = 2
a = πr²
a = π(2²)
a = 4π