Question

Need math help (last one wouldn't let me upload pic)

Answer 1

`\text{Area of the figure}=54\text{ unit}^2`

Explanation:

Please find the attachment.

Let us divide our given image in several parts and then we will find area of different parts.

First of all let us find the area of our red rectangle with side lengths 6 units and 7 units.

`\text{Area of rectangle}=\text{Length*Width}`

`\text{Area of red rectangle part}=6\text{ units}* 7\text{ units}`

`\text{Area of red rectangle part}=42\text{ units}^2`

Now let us find area of yellow triangle on the top of red rectangle. We can see that base of triangle is 6 units and height is 1 unit.

`\text{Area of triangle}=(1)/(2)* \text{Base*Height}`

`\text{Area of triangle}=(1)/(2)* \text{6 units *1 unit}`

`\text{Area of triangle}=3\text{ unit}^2`

Let us find the area of green triangle.

`\text{Area of green triangle}=(1)/(2)* \text{3 units *2 units}`

`\text{Area of green triangle}=3\text{ unit}^2`

Now we will find the area of blue triangle, whose base is 6 units and height is 2 units.

`\text{Area of blue triangle}=(1)/(2)* \text{6 units *2 units}`

`\text{Area of blue triangle}=6\text{ units}^2`

Let us add all these areas to find the area of our figure.

`\text{Area of the figure}=42\text{ units}^2+3\text{ unit}^2+3\text{ unit}^2+6\text{ unit}^2`

`\text{Area of the figure}=(42+3+3+6)\text{ unit}^2`

`\text{Area of the figure}=54\text{ unit}^2`

Therefore, area of our given figure is 54 square units.