8.03 Area of composite shapes
Consider the figure below:
Find the area of rectangle B.
Calculate the total area of the composite shape.
Find the shaded area in the figure below. Note that all measurements are in centimetres.
Consider the following figure:
Find the value of x.
Find the area of the shaded region.
Find the area of the following composite shapes:
Find the area of the shaded region in the following figures:
Find the shaded area of the following figures, correct to one decimal place:
Find the area of the arch below. Round your answer to two decimal places.
For the following circles, find:
The fraction of the circle's area covered by the sector
The area of the sector, correct to one decimal place.
Find the shaded area of the following figures, correct to one decimal place:
Find the shaded area of the following figures, correct to two decimal places:
In the figure shown, a chord is drawn so that it cuts through a circle:
Find the shaded area, correct to two decimal places.
Consider the figure shown:
Find the length of the diameter of the semicircle. Round your answer correct to two decimal places.
Find the area of the entire figure, correct to one decimal place.
Find the shaded area of the shape below. Round your answer to two decimal places.
Consider the figure below where the diameter of the semicircle is 17 \text{ cm}:
Find the perpendicular height of the parallelogram, correct to three decimal places.
Hence find the area of the shape, correct to two decimal places.
A piece of origami paper, orginally in the shape of a parallelogram, is folded along its shortest diagonal as shown.
What is the total area covered by the folded paper?
Lachlan designs a plot of land which contains his house and garden as shown in the diagram:
Find the total area of the plot of land.
Find the area of the garden.
The figure shows a plan of a dining room floor, which is to be tiled with slate tiles.
Calculate the area to be tiled. Round your answer to the nearest metre squared.
If the cost of tiling is \$10/m^2, how much will it cost to tile the dining room floor?
Luke wants to wallpaper two walls each measuring 3.9 \text{ m} high and 9.75 \text{ m} wide. One of the walls includes a doorway measuring 0.8 \text{ m} wide and 1.6 \text{ m} high.
Find the total area to be wallpapered.
If each roll of wallpaper covers an area of 10 \text{ m}^{2}, calculate the number of full rolls Luke must buy to cover the entire area.
A farmer is going to fertilise his paddock, which has the following shape:
Find the area of the paddock.
If it takes 150\text{ kg} of fertiliser to fertilise 100 square metres, how many kilograms of fertiliser should the farmer purchase?
The back cover of a mobile phone is shown in the following diagram. The rounded corners are quadrants:
Find the area of the back cover, excluding the circular camera lens. Round your answer to two decimal places.
A circular metal plate of diameter 2 metres, has 65 holes of diameter 5\text{ cm} drilled into it. Find the remaining area of the metal plate in square metres. Round your answer to two decimal places.
The diagram on the right shows a landscaping plan with the garden at the top bordered by a circular arc and the property boundary.
Find the area of the lawn in square metres.
Find the area of the garden in square metres. Round your answer to two decimal places.
If roll-on lawn costs \$12 per square metre, how much will it cost to cover the lawn and the garden?
Find the paved area in square metres. Round your answer to two decimal places.
Paving costs \$100 per square metre. Find the cost to pave the paved area.
A simple t-shirt pattern has the dimensions given in the diagram below, with a semicircular neck hole in the front piece only:
Find the area of the back of the t-shirt.
Find the area of the front of the t-shirt, to one decimal place.
If the front and back pieces are both cut from two rectangular pieces of fabric with dimensions 90\text{ cm} by 80\text{ cm}, how much fabric is wasted? Round your answer to the nearest square centimetre.
The fabric costs \$8 per metre length, where one metre length is a piece of fabric with width 80\text{ cm} and length 100\text{ cm}. If the t-shirt pieces are cut out of two 0.9 metre lengths as in part (c), how much will the fabric cost for 100 t-shirts?
A square has a quarter of a circle attached to one of its sides. The square has side length 9 \text{ cm} and the quarter of a circle has radius equal to the sides of the square. Find the total area, correct to two decimal places.
Tina, Brad, and Homer are designing a logo for their astronomy club.
Brad proposes that their logo should be in the shape of an annulus to represent an eclipse, as shown in the diagram:
Find the area of the annulus in the logo, correct to two decimal places.
Tina likes this idea but proposes that they shift the hole in the annulus to the side so that it better resembles an eclipse, as shown in the diagram:
Brad claims that this will change the area of the annulus. Is he correct? Explain your answer.
Homer claims that the logo will no longer be an annulus. Is he correct? Explain your answer.
