Answer:
See Explanation
Step-by-step explanation:
8. (1)
Area of trapezoid = 1/2(sum of || sides) *perpendicular distance
36 =1/2(x+ y) * 6
36 = ((x + y)*3
36/3 = x + y
12 = x + y
x + y = 12.... (1)
8(2)
It is given that:
x = 2y....(2)
From equations (1) & (2)
2y + y = 12
3y = 12
y = 12/3
y = 4
From equation (2)
x = 2y = 2*4
x = 8
9.
Area of square = 1 square m
Side of square = 1 m
Area of circle = 1 square m
Step-by-step explanation:
The shape of the new pizza must meet the conditions:
For simplicity, I will choose a polygon with 5 sides (a pentagon), and I will use 2 right angles (a "house" shape).
Split the pentagon into a rectangle on bottom and triangle on top. If we cut the rectangle into 8 pieces like a regular pizza, and the triangle in half, we get 10 triangles.
Now we just need to figure out the dimensions. The area of a 14" circular pizza is:
A = πr²
A = π (7 in)²
A ≈ 154 in²
That means the area of each triangle slice needs to be 15.4 in². If we make the total width of the pentagon 14", then the width of each triangle is 7", and the height of each triangle is:
A = ½ bh
15.4 in² = ½ (7 in) h
h = 4.4 in
Which makes the total height of the pentagon 3h = 13.2 in.
So, our 13.2" × 14" pentagon has at least 5 sides, is irregular, has the same area as a 14" diameter circle, fits in a 14⅛" × 14⅛" square, and can be divided into 8-12 equal pieces.
Of course, there are many possible solutions. This is just one way.
