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jasenka [17]
3 years ago
9

PLEASE HELPPP!!!!!!!!!!!!!

Mathematics
1 answer:
Leto [7]3 years ago
7 0

For this case we have:

Question 1:

According to Heron's formula, the area of ​​a triangle is given by:

A=\sqrt{(s(s-a)(s-b)(s-c))}

Where a, b and c are the sides of the triangle and s is the semi-perimeter of the triangle given by:

s=\frac{(a+b+c)}{2}

Let:

a = 20mm\\b = 23mm\\c = 27mm

We have s:

s=\frac{(20+23+27)}{2}\\s=\frac{70}{2}\\s=35

Substituting in the formula of the area:

A=\sqrt{(35(35-20)(35-23)(35-27))}\\A=\sqrt{(35(15)(12)(8))}\\A=\sqrt{(50400)}\\A=224.5mm^2

Thus, the area of ​​the triangle is A = 224.5mm ^ 2

Answer:

A = 224.5mm ^ 2

Question 2:

The area of ​​a traingule can be expressed as:

A=\frac{(b*h)}{2}

Where:

b: Base of the triangle

h: Triangle height

Let:

b = 20m\\h = 18m

Substituting the values ​​in the expression we have:

A=\frac{(20*18)}{2}\\A=\frac{360}{2}\\A=180m^2

Thus, the area of ​​the triangle is A = 180m ^ 2

Answer:

A = 180m ^ 2

Question 3:

It is known that the area of ​​a rectangle is given by:

A = l * w

Where:

l: It is the length of the rectangle

w: It is the width of the rectangle

So:

l = 9 feet\\w = 8 feet

Substituting:

A = (9 * 8) feet ^ 2\\A = 72 feet ^ 2

Thus, the area of ​​Laura's carpet is given by A = 72 feet ^ 2

Answer:

A = 72 feet ^ 2

Question 4:

We must take out the area of ​​the outer wall, given by a rectangle, then:

A = l * a

Where:

l: It is the length of the rectangle

a: It is the height of the rectangle

We have:

l = 48 feet\\a = 9 feet

Substituting in the formula we have:

A = (48 * 9) feet ^ 2\\A = 432ft ^ 2

Thus, the area of ​​the exterior wall is given by: A = 432 feet ^ 2

432ft ^ 2> 400ft ^ 2

So, a can of paint is not enough to cover the exterior wall.

Answer:

A can of paint is not enough to cover the exterior wall.

Question 5:

A regular hexagon is formed by 6 equal triangles. The area of ​​the hexagon is given by:

A=\frac{(perimeter* apothem)}{2}

Where the perimeter is given by the sum of the sides, that is:

perimeter = (10 + 10 + 10 + 10 + 10 + 10) cm\\perimeter = 60cm

And the apothem is the height of each of the triangles that make up the hexagon, that is:

apothem = 5cm

Substituting in the formula:

A=\frac{(60*5)}{2}\\A=\frac{300}{2}\\A=150cm^2

Thus, the area of ​​the hexagon is A = 150cm ^ 2

Answer:

A = 150cm ^ 2


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