Please I need help with this question.No 22. Is very important.Thank you.

Mathematics

1 answer:

kvv77 [185]4 years ago

6 0

Answer:

C. $132m^3$

Step-by-step explanation:

Height = 4

Length = 6

Breadth = 7

Note : We were asked to find volume of the cuboid

Since, it has a base in the shape of a right angle triangle , we need to find the Area of the trapezium before calculating the total volume.

Step 1

Find the area of the trapezium

Area of a trapezium = $\frac{1}{2} (a+b)h$

$\frac{1}{2} (4+7)*4$

$\frac{1}{2} (11)4\\$

$\frac{1}{2} *44\\= 22$

Step 2

Calculate the volume of the cuboid

Volume of a cuboid =length× breadth × height

In this case , the volume will be our length × Area of a trapezium

V= 6 × 22

V = $132m^3$

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Without plotting points, let M=(-2,-1), N=(3,1), M'= (0,2), and N'=(5, 4). Without using the distanceformula, show that segments

kramer

Given:

M=(x1, y1)=(-2,-1),

N=(x2, y2)=(3,1),

M'=(x3, y3)= (0,2),

N'=(x4, y4)=(5, 4).

We can prove MN and M'N' have the same length by proving that the points form the vertices of a parallelogram.

For a parallelogram, opposite sides are equal

If we prove that the quadrilateral MNN'M' forms a parallellogram, then MN and M'N' will be the oppposite sides. So, we can prove that MN=M'N'.

To prove MNN'M' is a parallelogram, we have to first prove that two pairs of opposite sides are parallel,

Slope of MN= Slope of M'N'.

Slope of MM'=NN'.

$\begin{gathered} \text{Slope of MN=}\frac{y2-y1}{x2-x1} \\ =\frac{1-(-1)}{3-(-2)} \\ =\frac{2}{5} \\ \text{Slope of M'N'=}\frac{y4-y3}{x4-x3} \\ =\frac{4-2}{5-0} \\ =\frac{2}{5} \end{gathered}$

Hence, slope of MN=Slope of M'N' and therefore, MN parallel to M'N'

$\begin{gathered} \text{Slope of MM'=}\frac{y3-y1}{x3-x1} \\ =\frac{4-(-1)}{5-(-2)} \\ =\frac{3}{2} \\ \text{Slope of NN'=}\frac{y4-y2}{x4-x2} \\ =\frac{4-1}{5-3} \\ =\frac{3}{2} \end{gathered}$

Hence, slope of MM'=Slope of NN' nd therefore, MM' parallel to NN'.

Since both pairs of opposite sides of MNN'M' are parallel, MM'N'N is a parallelogram.

Since the opposite sides are of equal length in a parallelogram, it is proved that segments MN and M'N' have the same length.