Question

A city wants to create a garden according to the plan below. Caculate the area of the garden

Answer 1

Looking at the plan below. We can see that the plan has been divided into a few sections: (Refer at the attached image)

Summing up the areas of each individual shapes we can get the total area of the garden.

Lets start with the triangular shape:

The length of the base of the triangle is 6 meters, the height of the triangle is 8 meters.

Using the formula for the area of triangle $=\frac{1}{2} \times base \times height$

Plugging the values of base and height we get:

Area $=\frac{1}{2} \times 6 \times 8=24$

So the area of triangular section is 24 square meters. (first section)

Now we can see that if we could divide the other compound shape into two sections we get a rectangle and a quadrilateral.

Now the length of the rectangular section is 12 meters and the width of the rectangular section is 8 meters.

So, the area of rectangular section is $= length \times width$

Plugging the values of length and width, we get:

$=12\times 8=96$ square meters

So the area of rectangular section is 96 square meters. (second section)

Now we have another section whose length and width is 8 meters. So we will calculate the area of square first:

Area of square section $=8\times 8=64$ square meters.

But there is a little triangular part that has been cut out or not included in the plan.

Area of that triangular section $=\frac{1}{2}\times base \times height$

The base length of that triangular section is 3 meters and height is 4 meters. So plugging the values we get:

$\frac{1}{2} \times 3\times 4=6$ square meters.

We need to subtract this area from the area of square, we get:

$64-6=58$ square meters

So the area of third section is 58 square meters. (third section)

Now, the total area of garden can be obtained by summing the area of all the three sections, we get:

$24+96+58=178$ square meters

Therefore the area of garden is 178 square meters.