8.02 Area
Find the area of the following:
Find the side length of the given square:
Find the length of each side of a square with an area of:
Find the perimeter of a square with an area of 49 \text{ cm}^2.
Find the area of a square with a perimeter of 8 \text{ cm}.
Find the area of a rectangle with a length of 12 \text{ cm} and a width of 5 \text{ cm}.
If the area of a rectangle is 99 \text{ cm}^2 and its width is 9 \text{ cm}, find its length.
Find the area of the following triangles:
Find the area, A, of a triangle with base b of 6 \text{ m} and height h of 12 \text{ m}.
Find the value of b if the area of the following triangle is 120 \text{ mm}^2:
Find the value of b if the area of the following triangle is 32 \text{ cm}^2:
Find the area of the following parallelograms:
Find the value of x in the following parallelogram, given that its area is 255 square units:
Find the base length, l, of a parallelogram with area of 96 \text{ cm}^2 and perpendicular height of 8\text{ cm.}
Find the perpendicular height, h, of a parallelogram with area of 84 \text{ cm}^2 and a base length of 6\text{ cm}.
Find the perpendicular height, h, of a parallelogram that has an area of 45 \text{ cm}^2 and a base length of 5 \text{ cm}
Find the area of the following trapeziums:
Find the height, h, if the area of the trapezium shown is 36 \text{ cm}^2:
Find the missing side length, b, if the area of the trapezium shown is 20 \text{ mm}^2:
Find the area of the following rhombuses:
Quadrilateral ABCD is a rhombus. AC is the diagonal x and BD is the diagonal y.
Find the area of the rhombus when:
x = 2 and y = 9
x = 6 and y = 16
Rhombus ABCD has an area of 55\,\text{cm}^2. If diagonal BD = 11 \,\text{cm}, and AC = x \,\text{cm}, find the value of x.
Find the area of the following kites:
Given the area of each of the following kites, find the length of diagonal k:
Area =56 \text{ cm}^2
Area =36 \text{ cm}^2
The area of a kite is 308 \text{ cm}^2 and one of the diagonals is 47 \text{ cm}.
If the length of the other diagonal is y \text{ cm}, find the exact value of y.
Find the area of the following circles correct to one decimal place:
Find the area of the following correct to one decimal place:
If the diameter of a circle is 24 \text{ cm}, find its area, correct to one decimal place.
A rectangular driveway is 8 \text{ m} long and 3 \text{ m} wide. Find the area of the driveway.
Katrina is digging a rectangular garden bed to plant some new hedging.
If the garden bed is 0.5 \text{ m} wide and 8 \text{ m} long, calculate the total area of the garden bed.
Each hedge plant fills an area that is the equivalent of 0.8 square metres. How many hedge plants are needed to fill Katrina’s garden bed?
A crop farmer trades 5 identical pieces of machinery, which have a market value of \$880\,000 each, for a square piece of land as shown in the scale drawing. The scale of the drawing is 1:3000.
Find the actual area of the square piece of land, in square metres.
Determine the total market value of the 5 pieces of machinery.
According to this exchange, find the value of the land per square metre, to the nearest dollar.
Consider a rectangular park that is 500 \text{ m} long and 300 \text{ m} wide:
Calculate the area of the park in square metres.
Calculate the area of the park in hectares. Note: 10\,000 \text{ m}^2=1 \text{ ha}.
Luke made a square mosaic that has side lengths of 3 metres. Luke decided to add a border to his mosaic, and now it has side lengths of 3.2 metres.
By how much has the area of the mosaic increased?
A family has 7.2 \text{ m}^2 of kitchen floor space for a rectangular bench.
If the width is fixed at 2 metres, and the bench is to take up all 7.2 \text{ m}^2, find the required length of the bench.
The kitchen bench will be made up of bench top pieces that measure 0.5 metres in width and 1.2 metres in length. Find the maximum number of bench top pieces that can be fitted along the width of the bench.
How many pieces of bench top pieces will be needed in total to create the bench top?
The kitchen floor is to be covered with tiles whose dimensions will be \dfrac{1}{8} the width of the bench, and \dfrac{1}{20} the length of the bench. How many tiles will be covered by the bench?
A farmer wants to cover a rectangular section of roofing that measures 5\dfrac{1}{2} \text{ m} by 4\dfrac{1}{2} \text{ m} with solar panels. Having received quotes from various solar panel suppliers, she estimates that the panels will cost \$300 per square metre to install.
Calculate the estimated cost of covering the section of roofing with solar panels.
A rectangular driveway is to be resurfaced with gravel. A 3 cubic metre load of gravel will cover 12 square metres of driveway, and costs \$6.
A scale drawing of the rectangular driveway is given. The actual length of the longest side of the driveway is 16 metres.
Determine the actual width of the driveway.
How many 3 cubic metre loads of gravel will be required to resurface the entire driveway?
Calculate the total cost of the gravel.
Sharon has purchased a rectangular piece of fabric measuring 12 \text{ m} in length and 7 \text{ m} in width.
Find the area of the largest triangular piece she can cut out from it.
A gutter running along the roof of a house has a cross-section in the shape of a triangle.
If the area of the cross-section is 50 \text{ cm}^2, and the length of the base of the gutter is 10 \text{ cm}, find the perpendicular height h of the gutter in metres.
Deep sea divers are scanning an area of the sea bed where a boat capsized. They want to get to point P, which is h metres above the sea bed.
At this point, they can cast a light out to view 9 metres across the sea bed and a cross sectional area of 45 \text{ m}^2 of water. From side-on, the light casts a shape that looks like the diagram below. The divers descend at a rate of 1.2 metres per second.
Find h, the distance of the divers from the sea bed at the point P.
If the divers were descending directly downwards, how high above the sea bed were they 6 seconds before they reached point P?
At the entrance of the Louvre museum is a glass structure in the shape of a square base pyramid.
A replica of this pyramid is to be built such that each triangular face of the pyramid measures 7.5 metres at the base, and has a perpendicular height of 10 metres.
The faces will be made up of identical triangular glass tiles tessellated to fit exactly on each face.
Find the total area that needs to be covered with the triangular glass tiles.
How many glass tiles will be needed in total if each triangular tile measures 15 \text{ cm} across the base and has a perpendicular height of 20 \text{ cm}?
A triangular-shaped field has sides of length 25 \text{ m}, 29 \text{ m} and 36 \text{ m}.
Use Heron's formula to find the area of the field.
Kenneth has been hired to plough the field and to erect fencing around its perimeter. If he charges \$4 per square metre for ploughing and \$7 per metre for fencing, how much does he charge in total?
The faces on a 4 sided die are all triangular. Each face has a base length of 13 \text{ mm} and a perpendicular height of 20 \text{ mm}. Find the area of one face of the die.
Buzz used some scrap paper to make a birthday card in the shape of a parallelogram. The base of the card is 18 \text{ cm} long, and the perpendicular height is 16 \text{ cm}.
Find the area of the card.
An area measuring 2016 \text{ cm}^2 is to be paved with identical tiles in the shape of parallelograms. Each tile measures 14 \text{ cm} along the base, and has a perpendicular height of 6 \text{ cm}.
Determine the area that each tile covers.
Calculate the number of tiles needed to cover the whole area.
Some car parks require the cars to park at an angle as shown.
The dimensions of the car park are as given, where each individual parking space has a perpendicular length of 4.9 \text{ m} and a width of 4.4 \text{ m.}
Determine the area needed to create an angled carpark suitable for 7 cars.
A quilt is made by sewing together 4 identical parallelograms as shown.
If the total area of the quilt is 1680 \text{ cm}^2, determine the perpendicular height of each parallelogram piece.
A roof in the shape of a parallelogram is to be entirely covered by identical solar panels that are also in the shape of a parallelogram. Each solar panel measures 1.8 \text{ m} along the longest side and has a perpendicular height of 0.9 \text{ m}.
Determine the area covered by one solar panel.
Determine the number of solar panels to be installed if the roof measures 58.32 \text{ m}^2 in area, and no part of the roof is to be left uncovered by solar panels.
A harbour has a trapezoidal pier with a perpendicular height of 8 \text{ m}. One base of the pier has a length of 9 \text{ m} and the other has a length of 5 \text{ m}.
Find the area of the pier.
The radius of a circular baking tray is 10 \text{ cm}. Find its area, correct to two decimal places.
The design attached is made using a large circle and two smaller circles of diameter 3\text{ cm}. Find the area of the shaded region correct to one decimal place.
