Mathematics, 20.06.2021 08:40 eddsworldfrantic

(High points) please solve with explanation

Answers: 3

Show answers

Answers

Answer from: Buttercream16

The area and the perimeter of the picture are:

Area = 160 cm^2Perimeter = 67.31 cm

Step-by-step explanation:

To find the area of that figure, you can find the area how if it was a rectangle and next subtract the area of the triangle in the upper part. The area of a rectangle could be found by the next formula:

Area of a rectangle = base * height

As you can see in the picture, the base is 16 cm and the height is 12 cm, then we replace in the formula:

Area of a rectangle = 16 cm * 12 cmArea of a rectangle = 192 cm^2

Now, we calculate the area of the triangle to subtract to the area we found and obtain the real area, the formula to obtain the area of a triangle is:

Area of a triangle = (base * height) / 2

The height of the triangle is 8 cm, and the base is 8 cm too, because you subtract to the base of the rectangle (16 cm) the measurements in the upper part (16 - 4 - 4 = 8), Now, we replace in the formula:

Area of a triangle = (8 cm * 8 cm) / 2Area of a triangle = (64 cm^2) / 2Area of a triangle = 32 cm^2

We subtract to the found area:

Area of the picture = 192 cm^2 - 32 cm^2Area of the picture = 160 cm^2

To find the perimeter, you must add all the sides of the picture, but, as you can see, there is a side that doesn't have the measurent, this is the hypotenuse of the triangle used before, but how we know the other sides, we can use Pythagorean theorem:

$a^{2}+b^{2}=c^{2}$

Where:

a = Opposite leg (8 cm)b = Adjacent leg (8 cm)

So, we replace in the theorem:

$a^{2}+b^{2}=c^{2}$ $(8 cm)^{2}+(8cm)^{2}=c^{2}$ (and we clear c) $\sqrt{(8 cm)^{2}+(8cm)^{2}} =c$ $\sqrt{64 cm^{2}+64cm^{2}} =c$ $\sqrt{128cm^{2}} =c$ c = 11.3137085 cmc ≅ 11.31 cm

At last, we add all the sides of the picture begining by the base and going by the left side:

Perimeter of the picture = 16 cm + 12 cm + 4 cm + 11.31 cm + 8 cm + 4 cm + 12 cmPerimeter of the picture = 67.31 cm approximately.

Answer from: Quest

given that triangle abc is transformed two times to get triangle

a"b"c"

first abc is transformed in to a'b'c' as follows:

the coordinates of a are (1,-1) and transformed into a'(-1,1)

similarly b (4,-2) became b'(-4,2) and

c(7,-2) became c'(-7,2)

i.e. (x,y) becomes (-x,-y)

this is nothing but reflection about a point here origin.

thus first transformation is reflection on the origin.

next is exactly shifting 3 units down

source:

Answer from: Quest

The coordinates of point a right now is (-3,-1) you have to multiply these coordinates by a factor of 2 to get (-6,-2)
If abcd is dilated by a factor of 2, the coordinate a would be: