Question

PLEASE HELP ME SOLVE THESE!!!

(if I have answers in the answer box in the photo please ignore the answer I have in it)

Answer 1

1. The volume of the composite figure is 10,164
`cm^3`.

2. The measure of ∠BCM is 59°.

3. The area of the given figure is 823.5
`in^2`.

4. The area of the given figure is 60
`yd^2`.

5. The area of the following figure is 22.5
`m^2`.

Explanation:

1. In order to make finding the composite figure's volume easier, we can separate the figure into two rectangular prisms, find the volume of each, and add them together. If we make a horizontal cut across the top of the large rectangular prism, we would have two rectangular prisms: One with the dimensions 23 cm × 10 cm × 42 cm, and one with the dimensions 3 cm × 4 cm × 42 cm. Their respective volumes would be 9,660
`cm^3` and 504
`cm^3`. Therefore, the composite figure's volume is 9,660 + 504 = 10,164
`cm^3.`

2. As ∠BCH and ∠MCD are vertical angles, we can conclude that 4g + 109 = 5g + 106. Based on this information, g is equivalent to 3, meaning both ∠BCH and ∠MCD have an angle measure of 121°. Since both angles form a straight angle with ∠BCM, we know that 121° plus the angle measure of ∠BCM is equivalent to 180°. Therefore, we can conclude that ∠BCM = 180 - 121 = 59°.

3. In order to make finding the area of the given figure easier, we can split the figure into three shapes: two rectangles and a triangle. The area of the large rectangle is 12 × 54 = 648
`in^2`, the area of the smaller rectangle is 12 × 9 = 108
`in^2`, and the area of the triangle is 15 × 9 ×
`(1)/(2)` = 67.5
`in^2`. Therefore, the area of the entire figure would be 648 + 108 + 67.5 = 823.5
`in^2`.

4. Like questions 1 and 3, we can cut the figure into a triangle, a rectangle, and a parallelogram in order to find the entire area easier. The area of the rectangle is 11 × 4 = 44
`yd^2`, and the area of the triangle is 5 × 4 ×
`(1)/(2)` = 10
`yd^2`. As for the parallelogram, it's important to note that in order to find the area of a parallelogram, you only need to multiply the length and the height together as you would for a rectangle. This is because you can cut any parallelogram and reshape it into a rectangle with the same dimensions, therefore the area of the parallelogram would be 3 × 2 = 6
`yd^2`. Lastly, the area of the entire given figure would be 44 + 10 + 6 = 60
`yd^2`.

5. Lastly, we are given a triangle and asked to find its area. An important information to keep in mind is that as long as you know a base length and the vertical height to that corresponding side, the formula to calculate the area of a triangle would still be
`(1)/(2) bh`. In the given triangle, the base length is 9 meters, and the vertical height is 5 meters. Therefore, the area of the following figure would be 22.5
`m^2`.

Have a great day! Feel free to let me know if you have any more questions :)