FIND THE AREA OF THE SHADED REGION USING POLYNOMIALS WORKSHEET

Find the area of shaded region :

Problem 1 :

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Problem 2 :

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Problem 3 :

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Problem 4 :

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Problem 5 :

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Problem 6 :

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Problem 7 :

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Problem 8 :

Solution

Problem 9 :

Find the area of the shaded region.

Solution

Problem 10 :

Kyle creates a canvas painting on a rectangular canvas with that is four inches longer than the height.

a) Write the polynomial expression, in simplified form that represents the area of the canvas.

b) Kyle adds 3 inch wide frame around all sides of his canvas. Write the polynomial expression, in simplified form that represents the total area of the frame.

Solution

Problem 11 :

Solution

Problem 12 :

Solution

Answers :

(1)  10x² square meter.

(2)  11x²/2 square meter.

(3)  4x² + 15x square meter.

(4)  8x+12 square meter.

(5)  2x² + 17x+ 21 square meter. 

(6)  3x²square meter. 

(7)   r²(π - 1) square meter. 

(8)   (bh/2) square meter. 

9)  18x² + 59x + 12

10)  i)  h² + 4h    ii)  h² + 16h + 60

11)  116x² + 53x

12)  66x³ + 40x² + 24x

Problem 1 :

A cylindrical tank has radius 1.5 m. What is the circumference of its base ?

Solution

Problem 2 :

A circular pond has diameter 8 m and needs to be fenced for the protection of children.

a) What length of fencing is required?

b) Fencing comes in 1 m lengths. How many lengths are needed?

c) What is the total cost of the fencing if each length costs $25.00?

Solution

Problem 3 :

A car wheel has a radius of 35 cm.

a)  What is the circumference of the wheel?

b)  If the wheel rotates 100 000 times, how far does the car travel?

Solution

Problem 4 :

A trundle wheel is used for measuring distances. The circumference of the wheel is exactly 1 m. Each time the wheel rotates through one complete turn a click sound is heard and a counter adds a meter to the total. What is the radius of this wheel?

Problem 5 :

A circular garden plot has circumference 12.65 m. Find its radius in meters, correct to the nearest centimetre.

Solution

Problem 6 :

An irrigation sprinkler sprays water over a field. The radius of the spray is 12.6 m. What area of the field is being watered?

Solution

Problem 7 :

The rope connecting a goat to a pole is 8 m long. What area of grass can the goat eat?

Solution

Problem 8 :

A circular hoop has a radius of 40 cm. Find the length of tubing needed to make the hoop.

Solution

Problem 9 :

6 identical metal discs are stamped out of an 18 cm by 12 cm sheet of copper as illustrated. What percentage of the copper is wasted

Solution

Problem 10 :

A table-top is shaped as illustrated. A cloth to protect the table-top from stains and heat is cut exactly the same size as the table-top. It is made from fabric 1.6 m wide and costs $18.40 per metre of length.

a) What length of fabric must be purchased?

b) Calculate the cost of the fabric.

c) Find the area of the cloth.

d) Calculate the amount of fabric that is wasted.

Solution

Problem 11 :

A circular mat has a diameter of 53 centimeters. Lily wants to sew a decorative braid around the mat. How many centimeters of braid does she need? Give your answer to the nearest tenth of a centimeter. Use 3.14 as an approximation of π.

Solution

Problem 12 :

A metalworker cuts out a large semicircle with a diameter of 28 centimeters. Then the metalworker cuts a smaller semicircle out of the larger one and removes it. The diameter of the semicircular piece that is removed is 14 centimeters. Find the distance around the shape after the smaller semicircle is removed. Use 22/7 as an approximation for π.

Solution

Problem 1 :

Find the area of the sector whose radius and central angle are 42 cm and 60° respectively. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution

Problem 2 :

Find the area of the sector that is outlined with the bold line. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution

Problem 3 :

Find the area of the sector that is outlined with the bold line. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution

Problem 4 :

In the diagram given below, LMN is a central angle and m∠LMN  =  78° and radius is 4 cm. find the area of sector LMN. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution

Problem 5 :

In circle C, if XCZ is a central angle and XYZ is an inscribed angle and m∠XYZ  =  58° and radius is 10 inches. Find the area of sector XCZ. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution

Problem 6 :

If QRS is a central angle and m∠QRS = 46°, m∠SRT = 80°, and diameter is 4 inches, then find the area of the shaded sector. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution

Problem 7 :

If the sector area of a sector intersecting Arc AB is 37 square cm and the radius is 11, then find the measure of Arc AB. (Take π = 3.14 and round your answer to the nearest whole number)

Solution

Problem 8 :

Find the area of the sector and the central angle formed by the sector whose radius is 21 cm and length of arc is 66 cm. (Take π = 3.14 and round your answer to the nearest whole number)

Solution

Problem 9 :

Find the area of the sector whose radius is 35 cm and perimeter is 147 cm.

Solution

Problem 10 :

If the sector area of a sector intersecting Arc AB is 43 square cm and the measure of Arc AB is 43°, then find the radius. (Take π = 3.14 and round your answer to one decimal place, if necessary)

Solution

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