A garden will be made up of a parallelogram, a rectangle and a triangle. The garden must have
an area of 500m2. Draw two possible gardens. Determine the dimensions of each part of the
garden, and justify your choice of these dimensions.
a rectangle 10x10
a right triangle with legs 20 and 20
a parallelogram with base 20 and height 10
area: 100+200+200
I'm sure you can come up with other scenarios.
Oh, so all we need to do is make combinations, so that all the area adds up to 500m2. Thank you Steve and Aryan!
Yes, thank you!
Yes, no problem at all. Your very welcome, and thank you!
Rectangle=
10x10
triangle=
20 x 20
parallelogram=
20x10
100m2 + 200m2 + 200m2 = 500m2
To determine the dimensions of each part of the garden and justify our choice, we need to consider the given area of 500m2 and the shapes involved: parallelogram, rectangle, and triangle.
Let's start by drawing the two possible gardens.
Possible Garden 1:
_______________
| |
| |
|_______|
Possible Garden 2:
_______________
| _________|
| |_________|
|_______|
In both gardens, the parallelogram, rectangle, and triangle will combine to form a larger shape.
For garden 1, we can make the parallelogram the largest shape, with the rectangle and triangle as smaller components within it. The dimensions can be as follows:
- Parallelogram dimensions:
- Base (b): 20m
- Height (h): 25m
- Rectangle dimensions:
- Length (l): 10m
- Width (w): 10m
- Triangle dimensions:
- Base (b): 15m
- Height (h): 10m
Justification for Garden 1 dimensions:
- The parallelogram is the largest shape, and its dimensions were chosen to achieve the required area. The base of 20m and height of 25m multiply to give an area of 500m2 (20m * 25m = 500m2).
- The rectangle and the triangle are smaller shapes placed inside the parallelogram to complete the garden design.
For garden 2, we can make the rectangle the largest shape and use the parallelogram and triangle as smaller components. The dimensions can be as follows:
- Rectangle dimensions:
- Length (l): 25m
- Width (w): 20m
- Parallelogram dimensions:
- Base (b): 10m
- Height (h): 15m
- Triangle dimensions:
- Base (b): 5m
- Height (h): 20m
Justification for Garden 2 dimensions:
- The rectangle is the largest shape, and its dimensions were chosen to achieve the required area. The length of 25m and width of 20m multiply to give an area of 500m2 (25m * 20m = 500m2).
- The parallelogram and triangle are smaller shapes placed inside the rectangle to complete the garden design.
These are two possible garden designs with the respective dimensions and justifications based on the given area requirement of 500m2.
Rectangle
Measurement:
Length = 20m
Width = 20m
Area = 200m2
An isosceles triangle
Measurement:
Base = 25m
Height = 16m
Area = 200m2
Parallelogram
Measurement:
Base: 25m
Height: 4m
Area = 100m2
Total Area = 200m2 + 200m2 + 100m2 = 500m2.