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2 years ago

Find the area of quadrilateral ABCD. Round the area to the nearest whole number, if necessary.

Mathematics

1 answer:

andrew11 [14]2 years ago

8 0

The area of the quadrilateral ABCD is 26 square units

<h3>How to find the area of quadrilateral ABCD?</h3>

The quadrilateral ABCD is a trapezoid, and it has the following parameters:

Parallel bases = BC and AD

Height = CE

The lengths of these sides can be calculated using

d = √[(x2 - x1)^2 +(y2 - y1)^2]

So, we have

BC = √[(0 - 4)^2 +(3 + 1)^2] = 4√2

AD = √[(-5 - 4)^2 +(4 + 5)^2] = 9√2

CE = √[(2 - 4)^2 +(-3 + 1)^2] = 2√2

The area of the quadrilateral ABCD is then calculated as

Area = 0.5 * (BC + AD) * CE

This gives

Area = 0.5 * (4√2 + 9√2) * 2√2

Evaluate

Area = 26

Hence, the area of the quadrilateral ABCD is 26 square units

You might be interested in

If tanA = 1/2 then evaluate cos A/sinA +sinA /1+cosA

Deffense [45]

Answer:

√5.

Step-by-step explanation:

Tan A = 1/2 means that the right triangle containing angle A has legs of length 1 and 2 units. So the hypotenuse = √(1^2 + 2^2) = √5 (using the Pythagoras theorem). The side opposite to < A = 1 unit and the adjacent side = 2 (as tan = opposite / adjacent).

so cos A = adjacent / hypotenuse = 2/√5.

and sin A = opposite / hypotenuse = 1 / √5

cos A / sin A = 2/√5 / 1/ √5 = 2.

sin A / (1 + cos A) = 1/√5 (1 + 2/ √5)

= 1 / √5 ( (√5 + 2) /√5)

= 1 / (√5 + 2)

So the answer is:

2 + 1 /(√5 + 2).

We can simplify it further by multiplying top and bottom of the fraction by the complement of √5 + 2 which is √5 - 2.

2 + 1 / (√5 + 2)

= 2(√5 + 2) + 1 / (√5 + 2 )

= { 2(√5 + 2) + 1 } / (√5 + 2)

Multiplying this by √5 - 2 / √5 - 2 we get:

(2(5 - 4) + √5 - 2) / (5 -4)

= 2 + √5 - 2 / 1

= √5.

3 0

3 years ago

Can someone help me with these problems? The majority of them I have answers but I don't understand them. Thanks!

zaharov [31]

Question 1:

The area of the triangle is $9\frac{5}{8}$ cm², if you want it rounded to the nearest whole number it will be 10 cm²

Question 2:

The area of the parallelogram is 304.5 m²

Question 3:

The ratio of grilled chicken salads sold to the total number of lunches sold is 1 : 3 in the simplest form

Question 4:

The ratio of odd to even digits in the following number: 7,208,631

is 3 : 4

Question 5:

5 tons is equal to 10,000 pounds

Question 6:

A table measures 3 feet across is 36 inches across

Step-by-step explanation:

Question 1:

The formula of the area of a triangle is $A=\frac{1}{2}bh$ , where

b is the base of the triangle
h is the height of the triangle

∵ The base of the triangle = $5\frac{1}{2}$ cm

∵ The height of the triangle = $3\frac{1}{2}$ cm

- Change the mixed numbers to improper fractions

∵ $5\frac{1}{2}$ = $\frac{(5*2)+1}{2}=\frac{11}{2}$

∵ $3\frac{1}{2}$ = $\frac{(3*2)+1}{2}=\frac{7}{2}$

∴ $A=\frac{1}{2}(\frac{11}{2})(\frac{7}{2})=\frac{77}{8}$ cm²

- To change the improper fraction to mixed number divide 77 by 8

∵ 77 ÷ 8 = 9 and remainder 5 (8 × 9 = 72 , 77 - 72 = 5)

∴ 77 ÷ 8 = $9\frac{5}{8}$

∴ $A=9\frac{5}{8}$ cm²

The area of the triangle is $9\frac{5}{8}$ cm²

If you want to round it to the nearest whole number the area will

be 10 cm²

Question 2:

The formula of the area of a parallelogram is A = b h , where

b is the base of the parallelogram
h is the height of this base of the parallelogram

∵ The base of the parallelogram = 14.5 m

∵ Its height = 21 m

∵ A = b h

∴ A = 14.5 × 21 = 304.5 m²

The area of the parallelogram is 304.5 m²

Question 3:

∵ The cafeteria sold 200 grilled cheese sandwiches, 100 tacos, and

150 grilled chicken salads

∴ The cafeteria sold = 200 + 100 + 150 = 450 lunches

- To find the ratio between the grilled chicken salads sold to the total

number of lunches sold divide them and simplify the answer to the

lowest term

→ G.C.S : Lunches

→ 150 : 450 ⇒ divide both by 10

→ 15 : 45 ⇒ divide both by 5

→ 3 : 9 ⇒ divide both by 3

→ 1 : 3

The ratio of grilled chicken salads sold to the total number of lunches sold is 1 : 3 in the simplest form

Question 4:

The even numbers are the numbers whose one digit is 0 , 2 , 4 , 6 , 8

The odd numbers are the numbers whose one digit is 1 , 3 , 5 , 7 , 9

∵ The number is 7,208,631

∵ The odd digits are 7 , 3 , 1

∴ There are 3 odd digits

∵ The even numbers are 2 , 0 , 8 , 6

∴ there are 4 even digits

∴ The ratio of odd to even digits is 3 : 4

The ratio of odd to even digits in the following number: 7,208,631

is 3 : 4

Question 5:

∵ One ton is equal to 2000 pounds

∵ There are 5 tons

→ Ton : Pound

→ 1 : 2000

→ 5 : x

Use the cross multiplication

∵ 1 × x = 5 × 2000

∴ x = 10,000 pounds

5 tons is equal to 10,000 pounds

Question 6:

∵ A table measures 3 feet across

∵ 1 foot = 12 inches

∴ 3 × 12 = 36 inches

A table measures 3 feet across is 36 inches across

Learn more:

You can learn more about ratio in brainly.com/question/10781917

#LearnwithBrainly

6 0

3 years ago

Write an expression to represent susans age in three years when a represents her present age.

Zarrin [17]

Well, since a is Susan’s current age, we would add three to a to get her age in three years
So our expression would be:
a + 3

4 0

3 years ago

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Ali’s dog weighs 8 times as much as her cat. Together, the two pets weigh 54 pounds. How much does Ali’s dog weigh?

baherus [9]

Ali's dog weighs 48 pounds.

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3 years ago

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4x^2-20=5 solve by using the square root property

riadik2000 [5.3K]

Step-by-step explanation:

4x^2 - 20 = 5

4x^2 -25 = 0

4x^2 = 25

2x = 5, or -5

x = 5/2 , or -5/2

7 0

3 years ago