Question

There is a polygon that look like the letter j and I need to find the area in the J which has 5 inches on top 12 inches to the right 4 inches on the tip and 5 inches right over the top

Answer 1

The total area is 70 sq cm.

To find the area of the J-shaped polygon, we can break it down into two parts: a rectangle and a right-angled triangle.

1. Rectangle:

- The top part of the J has a length of 5 inches.

- The width of the rectangle is the horizontal distance from the top part to the tip, which is 12 inches.

The area of the rectangle
`(\( A_{\text{rectangle}} \))` is given by:

`\[ A_{\text{rectangle}} = \text{length} * \text{width} \]`

`\[ A_{\text{rectangle}} = 5 \, \text{in} * 12 \, \text{in} \]`

2. Triangle:

- The right-angled triangle has a base of 4 inches (the tip of the J) and a height of 5 inches (the vertical distance from the tip to the top).

The area of the triangle
`(\( A_{\text{triangle}} \))` is given by:

`\[ A_{\text{triangle}} = (1)/(2) * \text{base} * \text{height} \]`

`\[ A_{\text{triangle}} = (1)/(2) * 4 \, \text{in} * 5 \, \text{in} \]`

Now, you can find the total area
`(\( A_{\text{total}} \))` by adding the area of the rectangle and the area of the triangle:

`\[ A_{\text{total}} = A_{\text{rectangle}} + A_{\text{triangle}} \]`

`\[ A_{\text{total}} = (5 \, \text{in} * 12 \, \text{in}) + \left((1)/(2) * 4 \, \text{in} * 5 \, \text{in}\right) \]`

Therefore, the total area is 70 sq cm.

The probable question may be: "There is a polygon that looks like the letter j which has 5 inches on top 12 inches to the right 4 inches on the tip and 5 inches right over the top. Find the total area of this J-shaped Polygon"