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3 years ago

What is the LATERAL surface area of the rectangular pyramid below???

Mathematics

2 answers:

kherson [118]3 years ago

5 0

684 ft²

Area of rectangle :-

A = 18 ft * 20ft

A = 360 ft²

Area of 2 triangles :-

A = 2 * 8ft * 18 ft * 1/2

A = 144 ft²

Area of 2 triangles :-

A = 2 * 1/2 * 9ft * 20ft

A = 180 ft²

Total Area :-

A = ( 360 + 144 + 180 ) ft²

A = 684 ft²

emmasim [6.3K]3 years ago

4 0

Answer:

684 sq.ft

Step-by-step explanation:

(1) The base area of the pyramid is 18x20=360 sq.ft

(2) The Triangles of the pyramid:

1. There are two kinds of the triangles.

2. Smaller one: 18x8/2 (base times height divide 2)=72 sq.ft

3. Bigger one: 20x9/2=90 sq.ft

4. There are two of them so 72+72+90+90=324 sq.ft

And so 360+324=684 sq.ft.

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A container in the shape of a square-based prism has a volume of 2744 cm'. What dimensions give the

Vinvika [58]

Answer:

The dimensions that give the minimum surface area are:

Length = 14cm

width = 14cm

height = 14cm

And the minimum surface is:

S = 1,176 cm^2

Step-by-step explanation:

A regular rectangular prism has the measures: length L, width W and height H.

The volume of this prism is:

V = L*W*H

The surface of this prism is:

S = 2*(L*W + H*L + H*W)

If the base of the prism is a square, then we have L = W

Then the equations become:

V = L*L*H = L^2*H

S = 2*(L^2 + 2*H*L)

We know that the volume of the figure is 2744 cm^3

Then:

V = 2744 cm^3 = H*(L^2)

In this equation, we can isolate H.

H = (2744 cm^3)/(L^2)

Now we can replace this on the surface equation:

S = 2*(L^2 + 2*L* (2744 cm^3)/(L^2))

S = 2*L^2 + 4(2744 cm^3)/L

Now we want to minimize the surface area, then we need to find the zeros of the first derivative of S.

S' = 2*(2*L) - 4*(2744 cm^3)/L^2

This is equal to zero when:

0 = 2*(2*L) - 4*(2744 cm^3)/L^2

0 = 4*L*L^2 - 4*(2744 cm^3)

4*(2744 cm^3) = 4*L^3

2744 cm^3 = L^3

∛(2744 cm^3) = L = 14cm

Then the length of the base that minimizes the surface is L = 14.

Then we have:

H = (2744 cm^3)/(L^2) = (2744 cm^3)/(14cm)^2 = 14cm

Then the surface is:

S = 2*(L^2 + 2*L*H) = 2*( (14cm)^2 + 2*(14cm)*(14cm)) = 1,176 cm^2

8 0

2 years ago

PLEASE HELPPPPPP<br>what is a semicirles permitier if the diameter is 4

trapecia [35]

The straight edge of the semicircle is 4 units, as this is this the diameter.

The circumference of the full circle is

C = pi*d = pi*4 = 4pi

which is the distance around the full circle (aka circle's perimeter)

So half of this is 4pi/2 = 2pi

Add this onto the straight edge length to get 4+2pi as the exact distance around the entire semicircle. This includes both straight and curved portions.

If you use the approximation pi = 3.14, then 4+2*pi = 4+2*3.14 = 10.28 is the approximate answer. To get a more accurate answer, use more decimal digits in pi.

---------------------------------------------------------

In summary,

exact answer in terms of pi is 4+2pi units

approximate answer is roughly 10.28 units (using pi = 3.14)

6 0

3 years ago

Please help me out with this question thank you ❤️

devlian [24]

Answer:

log

→

Step-by-step explanation:

7 0

3 years ago

The length of a 200 square foot rectangular vegetable garden is 4feet less than twice the width. Find the length and width of th

inna [77]

Answer:

Length = 18.099 ft

Width = 11.049 ft

Step-by-step explanation:

let the length of the field be x ft

and the width be y ft

as per the condition given in problem

x=2y-4 -----------(A)

Also the area is given as 200 sqft

Hence

xy=200

Hence from A we get

y(2y-4)=200

taking 2 as GCF out

2y(y-2)=200

Dividing both sides by 2 we get

$y(y-2)=100$

$y^2-2y=100$

subtracting 100 from both sides

$y^2-2y-100=0$

Now we solve the above equation with the help of Quadratic formula which is given in the image attached with this for any equation in form

$ax^2+bx+c=0$

Here in our case

a=1

b=-1

c=-100

Putting those values in the formula and solving them for y

$y=\frac{-(-2)+\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

$y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

Solving first

$y=\frac{2+\sqrt{4+400}{2}$

$y=\frac{2+\sqrt{404}{2}$

$y=\frac{2+20.099}{2}$

$y=\frac{22.099}{2}$

$y=11.049$

Solving second one

$y=\frac{-(-2)-\sqrt{(-2)^2-4 \times (-1) \times 100}}{2 \time 1}$

$y=\frac{2-\sqrt{4+400}{2}$

$y=\frac{2-\sqrt{404}{2}$

$y=\frac{2-20.099}{2}$

$y=\frac{-18.99}{2}$

$y=-9.045$

Which is wrong as the width can not be in negative

Our width of the field is

y=11.099

Hence the length will be

x=2y-4

x=2(11.049)-4

x=22.099-4

x=18.099

Hence our length x and width y :

Length = 18.099 ft

Width = 11.049 ft

4 0

3 years ago

Construct a truth table for the statement: (p v q) v (~p ^ q) -> q

Gnom [1K]

Step-by-step explanation:

We have the following statement $(p\lor q)\lor(\lnot p \land q) \rightarrow q$

A truth table shows how the truth or falsity of a compound statement depends on the truth or falsity of the simple statements from which it's constructed.

The simple statements from the statement given are:

$\lnot p$ , $p\lor q$ , $\lnot p \land q$ , and $(p\lor q)\lor(\lnot p \land q)$

This is the truth table.

8 0

3 years ago