10.05 Area of parallelograms
For the following parallelogram:
If the parallelogram is formed into a rectangle, find:
The length of the rectangle.
The width of the rectangle.
Find the area of the parallelogram.
Find the area of the following parallelogram by rearranging it into a rectangle:
Consider the following parallelogram:
Identify the base and the height.
Find the area of the given parallelogram.
Find the area of the following parallelograms:
Find the area of the parallelograms with the following dimensions:
The base is 5\text{ mm}, and the perpendicular height is 2\text{ mm}.
The base is 15\text{ cm} and the perpendicular height is 7\text{ cm}.
Find the value of b or h in the following parallelograms:
Area =36\text{ cm}^2
Area =35\text{ m}^2
Find the base length of a parallelogram whose area is 108\text{ cm}^2 and perpendicular height is 9\text{ cm}.
Find the perpendicular height of a parallelogram whose area is 99\text{ m}^2 and base is 9\text{ m}.
Determine whether the following could be the dimensions of a parallelogram with an area of 28\text{ mm}^2:
Base =1\text{ mm}, height =28\text{ mm}
Base =7\text{ mm}, height =4\text{ mm}
Base =4\text{ mm}, height =7\text{ mm}
Base =2\text{ mm}, height =28\text{ mm}
Complete the following table of base and height measurements for different parallelograms with an area of 60\text{ cm}^2:
| \text{Base (cm)} | 10 | 30 | |
|---|---|---|---|
| \text{Height (cm)} | 12 | ||
| \text{Area (cm}^2) | 60 | 60 | 60 |
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 length of 5.1\text{ m} and a width of 3.9\text{ m}. What area is needed to create an angled car park suitable for 7 cars?
The tile pattern shown is made up of two different parallelograms in a tessellated pattern.
Find the area covered by the smaller tiles.
Find the area covered by the larger tiles.
Calculate the total area covered.
James used some scrap paper to make a birthday card in the shape of a parallelogram. The base of the card is 17\text{ cm} long, and the perpendicular height is 16\text{ cm}. Find the area of the card.
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 1.2\text{ m} along the longest side and has a perpendicular height of 0.6\text{ m}.
Find the area covered by one solar panel.
Find the number of solar panels to be installed if the roof measures 23.04\text{ m}^2 in area, and no part of the roof is to be left uncovered by solar panels.
An area measuring 2280\text{ cm}^2 is to be paved with identical tiles in the shape of parallelograms. Each tile measures 12\text{ cm} along the base, and has a perpendicular height of 5\text{ cm}.
Find the area that each tile covers.
How many tiles are needed to cover the whole area?
A quilt is made by sewing together 4 identical parallelograms as shown in the following figure:
If the total area of the quilt is 1944\text{ cm}^2, calculate the perpendicular height of each parallelogram piece.
