Question

Work out the percentage of the area inside the square that is shaded.

Answer 1

55%.

Explanation:

Since we know that all sides of a square have equal length and perimeter of a square is 4 times the length of one side of square, so we can find length of each side of square by multiplying 40 by 4.

`\text{Each side length of square}=(40)/(4) =10`

Now we will find the area of our square with side length 10.

`\text{Area of square}=\text{(10 cm)}^(2)=100\text{ cm}^(2)`

Now we will find the area of shaded region by subtracting the non-shaded area of square from the total area of square. We can see that non-shaded part of our square is in form of two right triangle.

Let us find area of triangle whose base is 10 cm and height is 6 cm (10-4).

`\text{Area of horizontal base triangle}=(1)/(2)\cdot 10\cdot 6`

`\text{Area of horizontal base triangle}=5\cdot 6=30`

Now let us find area of triangle whose base is 10 cm (vertical) and height is 3 cm (10-7).

`\text{Area of horizontal base triangle}=(1)/(2)\cdot 10\cdot 3`

`\text{Area of horizontal base triangle}=5\cdot 3=15`

Now let us find area of shaded part inside square by subtracting area of two triangles from area of square.

`\text{Area of shaded part inside square}=100-(30+15)`

`\text{Area of shaded part inside square}=100-(45)`

`\text{Area of shaded part inside square}=55`

Therefore, area of shaded part inside square is
`55 cm^(2)`

Now let us find 55 is what percent of 100.

`\text{Percentage of shaded area inside square}=(55)/(100) \cdot 100`

`\text{Percentage of shaded area inside square}=55`

Therefore, 55% of the area inside the square is shaded.