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scoray [572]
3 years ago
9

What is the area of this trapezoid?

Mathematics
2 answers:
Nadusha1986 [10]3 years ago
7 0

Answer:

30 units²

Step-by-step explanation:

this ones kinda tricky but basically you need to dilate it all by 2 (to make the figure twice as big)

technically, it would be 7.5 units bc but bc of the dilation it'd be 30

liberstina [14]3 years ago
4 0

Answer:

7.5\:\text{square units}

Step-by-step explanation:

The area of a trapezoid is given by the average of the bases multiplied by the height.

What we're given:

  • Height of 3
  • Bases of 1 and 4

The average of the bases 1 and 4 is equal to \frac{4+1}{2}=\frac{5}{2}=2.5

Therefore, the area of the trapezoid is 2.5\cdot 3=\boxed{7.5\:\text{square units}}

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An art museum has a pentagon-shaped room. When drawn to scale on a coordinate grid, the corners of the room are points (18,20):
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Answer:

2\ gal

Step-by-step explanation:

we know that

the formula to calculate the distance between two points is equal to

d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}

we have

A(18,20),B(4,20),C(4,4),D(16.2),E(22.10)

step 1

Find the distance AB

we have

A(18,20),B(4,20)

substitute in the formula

d=\sqrt{(20-20)^{2}+(4-18)^{2}}

d=\sqrt{(0)^{2}+(-14)^{2}}

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step 2

Find the distance BC

we have

B(4,20),C(4,4)

substitute in the formula

d=\sqrt{(4-20)^{2}+(4-4)^{2}}

d=\sqrt{(-16)^{2}+(0)^{2}}

BC=16\ ft

step 3

Find the distance DE

we have

D(16.2),E(22.10)

substitute in the formula

d=\sqrt{(10-2)^{2}+(22-16)^{2}}

d=\sqrt{(8)^{2}+(6)^{2}}

d=\sqrt{100}

DE=10\ ft

step 4

Find the distance AE

we have

A(18,20),E(22.10)

substitute in the formula

d=\sqrt{(10-20)^{2}+(22-18)^{2}}

d=\sqrt{(-10)^{2}+(4)^{2}}

d=\sqrt{116}

AE=10.77\ ft

step 5

Find out the area of the four walls

To determine the area sum the length sides and multiply by the height of the walls

so

A=(AB+BC+DE+AE)h

substitute the given values

The height of the walls is 10 ft

A=(14+16+10+10.77)10

A=(50.77)10

A=507.7\ ft^2

step 6

Determine the number of gallons needed to paint the four walls

we know that

one gallon of paint is enough to cover 400 square feet

using proportion

\frac{1}{400}\ \frac{gal}{ft^2}=\frac{x}{507.7}\ \frac{gal}{ft^2}\\\\x=507.7/400\\\\x= 1.27\ gal

Round up

x=2\ gal

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