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3 years ago

A garden is made up of two squares and a quarter circle. What is the area of the garden?

Mathematics

1 answer:

Elanso [62]3 years ago

7 0

9514 1404 393

Answer:

100.27 ft^2

Step-by-step explanation:

The area of each square is ...

A = s^2 = (6 ft)^2 = 36 ft^2

The area of the 1/4 circle is ...

A = 1/4πr^2 = 1/4π(6 ft)^2 = 9π ft^2 ≈ 28.27 ft^2

The area of the garden is the sum of the areas of the quarter circle and the two squares:

A = 28.27 ft^2 + 2×36 ft^2 = 100.27 ft^2

The area of the garden is about 100.27 square feet.

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In the given figure △ABC ≅△DEC. Which of the following relations can be proven using CPCTC ?

Serhud [2]

Option B:

$\overline{A B}=\overline{D E}$

Solution:

In the given figure $\triangle A B C \cong \triangle D E C$ .

If two triangles are similar, then their corresponding sides and angles are equal.

By CPCTC, in $\triangle A B C \ \text{and}\ \triangle D E C$ ,

$\overline{AB }=\overline{DE}$ – – – – (1)

$\overline{B C}=\overline{EC}$ – – – – (2)

$\overline{ CA}=\overline{CD}$ – – – – (3)

$\angle ACB=\angle DCE$ – – – – (4)

$\angle ABC=\angle DEC$ – – – – (5)

$\angle BAC=\angle EDC$ – – – – (6)

Option A: $\overline{B C}=\overline{D C}$

By CPCTC proved in equation (2) $\overline{B C}=\overline{EC}$ .

Therefore $\overline{B C}\neq \overline{D C}$ . Option A is false.

Option B: $\overline{A B}=\overline{D E}$

By CPCTC proved in equation (1) $\overline{AB }=\overline{DE}$ .

Therefore Option B is true.

Option C: $\angle A C B=\angle D E C$

By CPCTC proved in equation (4) $\angle ACB=\angle DCE$ .

Therefore $\angle A C B\neq \angle D E C$ . Option C is false.

Option D: $\angle A B C=\angle E D C$

By CPCTC proved in equation (5) $\angle ABC=\angle DEC$ .

Therefore $\angle A B C\neq \angle E D C$ . Option D is false.

Hence Option B is the correct answer.

$\Rightarrow\overline{A B}=\overline{D E}$

5 0

3 years ago

Hal has a steel barrel with a diameter of 6 feet that can be filled to a depth of 4.6 feet with oil. What is the volume of the b

scoray [572]

Answer:

129.996 cubic feet

Step-by-step explanation:

Assuming that the barrel is a perfect cylinder, we can use the formula to find the volume:

$\pi(r)^2(h)$

First, we have to find the radius, which is:

D = 2r

So the radius is 3 feet, since it is half of the diameter. Then, we plug in the values.

$3.14(3)^2(4.6)$

Now, we solve. Exponents are first...

3.14(9)(4.6)

Now multiply left to right.

28.26(4.6)

129.996 cubic feet

Therefore, the barrel can hold 129.996 cubic feet of oil. Hope this helps you!

3 0

3 years ago

Please answer correctly and answer all questions I will give a heart please

NNADVOKAT [17]

Answer:

1 = A, D 2 = B, C, D . 3 = True . 5 = D . 11 = C, D E

Step-by-step explanation:

5 0

3 years ago

Factor completely, then place the factors in the proper location on the grid. 25a2 +9b2 + 30ab

sergij07 [2.7K]

Answer:

(5a+3b)(5a+3b) or SQ(5a+3b)

Step-by-step explanation:

Now you can plot by referring to the above factors

8 0

3 years ago

How many dominos are needed to complete the triangle?

solong [7]

Only 3 is needed

Step-by-step explanation:

5 0

2 years ago

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