Two pumps connected in parallel fail independently of one another on any given day. The probability that only the older pump wil
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SHAPE A
Shape A can be split into two shapes as shown in the diagram below. One is a rectangle and the other is an isosceles triangle. The dimension of the rectangle is 80×180 but we do not know the base of the triangle.
Area of rectangle = 80×180 = 14400
Base of rectangle can be worked out using the Pythagoras theorem
the base of the triangle = 2×25 = 50
Area of rectangle = 1/2(base)(height) = 0.5×50×60 = 1950
Total area of shape A = 1950 + 14400 = 16350
Tax = 16350÷100 = $163.50
Total perimeter of shape A = 80+80+180+65+65 = 470
SHAPE B
We split shape B into a parallelogram and a trapezium
Area of parallelogram = base × height = 250 × 30 = 7500
Area of trapezium =
×
=
×
Total area = 5600 + 7500 = 13100
Tax = 13100÷100 = $131
Perimeter = 250+250+35+35+100+40+80 = 790
SHAPE C
Shape C is an isosceles shape which allows us to split side bc into 100÷2=50. The diagram is shown in the third diagram.
Quadrilateral PODY = Quadrilaterla AXPO
Side CY =
Side PY = 50+38.1 = 88.1
Side DS =
(rounded to whole number)
Side OP = 100-77=23
Area of PODY =
Area of DCY =
Area of DCPO = 5418.15-1905 = 3513.15
Area of ABCD = 3513.15×2 = 7026.3
Tax = 7026.3÷100 = $70.263
Perimeter = 117+117+107+107+100 = 548
SHAPE D
Shape D can be split into a triangle and a trapezium as shown in the fourth diagram below
Area of triangle =
Area of trapezium =
Total area = 22500 + 160000 = 182500
Tax = 182500÷100 = $1825
Perimeter = 280+165+406+500+425 = 1776
Shape A can be split into two shapes as shown in the diagram below. One is a rectangle and the other is an isosceles triangle. The dimension of the rectangle is 80×180 but we do not know the base of the triangle.
Area of rectangle = 80×180 = 14400
Base of rectangle can be worked out using the Pythagoras theorem
the base of the triangle = 2×25 = 50
Area of rectangle = 1/2(base)(height) = 0.5×50×60 = 1950
Total area of shape A = 1950 + 14400 = 16350
Tax = 16350÷100 = $163.50
Total perimeter of shape A = 80+80+180+65+65 = 470
SHAPE B
We split shape B into a parallelogram and a trapezium
Area of parallelogram = base × height = 250 × 30 = 7500
Area of trapezium =
Total area = 5600 + 7500 = 13100
Tax = 13100÷100 = $131
Perimeter = 250+250+35+35+100+40+80 = 790
SHAPE C
Shape C is an isosceles shape which allows us to split side bc into 100÷2=50. The diagram is shown in the third diagram.
Quadrilateral PODY = Quadrilaterla AXPO
Side CY =
Side PY = 50+38.1 = 88.1
Side DS =
Side OP = 100-77=23
Area of PODY =
Area of DCY =
Area of DCPO = 5418.15-1905 = 3513.15
Area of ABCD = 3513.15×2 = 7026.3
Tax = 7026.3÷100 = $70.263
Perimeter = 117+117+107+107+100 = 548
SHAPE D
Shape D can be split into a triangle and a trapezium as shown in the fourth diagram below
Area of triangle =
Area of trapezium =
Total area = 22500 + 160000 = 182500
Tax = 182500÷100 = $1825
Perimeter = 280+165+406+500+425 = 1776