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arlik [135]
3 years ago
6

The vertices of rhombus DEFG are D(1, 4), E(4, 0), F(1, –4), and G(–2, 0).

Mathematics
2 answers:
musickatia [10]3 years ago
7 0
20 units im shure i took the test'

nirvana33 [79]3 years ago
4 0

Answer: Perimeter of the rhombus is 20 units.

Step-by-step explanation:

Since we have given that

The vertices of rhombus DEFG whose vertices are as follows:

D(1, 4), E(4, 0), F(1, –4), and G(–2, 0)

As shown in the figure below:

Distance between DE is given by

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\D=\sqrt{(4-1)^2+(0-4)^2}\\\\D=\sqrt{3^2+4^2}\\\\D=\sqrt{9+16}\\\\D=\sqrt{25}\\\\D=5\ units

Since it is a rhombus all sides will be equal to each other,

So, Perimeter of rhombus is given by

4\times Side\\\\=4\times 5\\\\=20\ units

Hence, Perimeter of the rhombus is 20 units.


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The length of the base edge of a pyramid with a regular hexagon base is represented as x. The height of the pyramid is 3 times l
sergij07 [2.7K]

Answer:

(a)

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(b)

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(c)

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(d)

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Step-by-step explanation:

We are given a regular hexagon pyramid

Since, it is regular hexagon

so, value of edge of all sides must be same

The length of the base edge of a pyramid with a regular hexagon base is represented as x

so, edge of base =x

b=x

Let's assume each blank spaces as a , b , c, d

we will find value for each spaces

(a)

The height of the pyramid is 3 times longer than the base edge

so, height =3*edge of base

height=3x

h=3x

(b)

Since, it is in units^2

so, it is given to find area

we know that

area of equilateral triangle is

=\frac{\sqrt{3} }{4} b^2

h=3x

b=x

now, we can plug values

A=\frac{\sqrt{3} }{4} x^2

(c)

we know that

there are six such triangles in the base of hexagon

So,

Area of base of hexagon = 6* (area of triangle)

Area of base of hexagon is

=6\times \frac{\sqrt{3} }{4} x^2

=\frac{3\sqrt{3} }{2} x^2

(d)

Volume=(1/3)* (Area of hexagon)*(height of pyramid)

now, we can plug values

Volume is

=\frac{1}{3}\times\frac{3\sqrt{3} }{2} x^2\times (3x)

V=\frac{3\sqrt{3} }{2} x^3 units^3


3 0
3 years ago
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