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LekaFEV [45]
3 years ago
13

The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal siz

e. A shade for the window will extend 4 inches beyond the perimeter of the window, shown by the dashed line around the window. Each square in the window has an area of 100 i n 2 . What is the area of the shade? Round your answer to the nearest whole number.

Mathematics
2 answers:
givi [52]3 years ago
8 0
Area of the window:
A ( window ) = 16  · 100 + 1/2 · 20² π = 1600 + 200 π = 2,228
A ( window + shade ) = 48  · 40 + 1/2 · 24² π = 2,824.32
A ( shade ) = 2,824.32 - 2,228 = 596.32 ≈ 596 in²
Answer:
Area of the shade is 596 in².
kirza4 [7]3 years ago
7 0

Answer:

<h2>The total area is 3016 square inches, approximately.</h2>

Step-by-step explanation:

The complete problem is attached.

The area of the window is separated in two parts, the semicircle and the square.

We know that each square has an area of 100 square inches, which means that the whole big square has an area of 1600 square inches, because there are 16 total squares.

Also, each side of each small square is (100)^{2} long, which is 10 inches. This means the diameter of the semicircle is 40 inches, and its area is

A_{semicircle} =\frac{\pi r^{2} }{2}=\frac{3.14(20)^{2}}{2}  = 628 in^{2}

Therefore, the area of the whole window is

A_{window}=1600+628 = 2228 in^{2}

Now, the shade is 4 inches beyond the perimeter, that means each side the new rectangle is

b=40+4+4=48\\h=40+4=44

Similarly, the radius of the new semicircle is

r=20+4=24

Then, we just have to find the new combined area.

A_{rectangle}=48(44)=2,112 in^{2}  \\A_{new \ semicircle}=\frac{3.14(24)^{2} }{2}=904.32

So, the total area of the shade is

A_{shade}=2112+904.32 = 3016 in^{2}

Therefore, the total area is 3016 square inches, approximately.

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3 years ago
Number 7 and 8 plz answer quickly
Flauer [41]

(7) m∠A = 52°

(8) m∠B = 117°

Solution:

(7) Let us first define the supplementary and complementary angles.

Supplementary angles: Two angles are said to be supplementary angles if their sum is add up to 180°

Complementary angles: Two angles are said to be complementary angles if their sum is add up to 90°

Given supplement of 142° = 180° – 142°

                                           = 38°

Complement of ∠A = Supplement of 142°

⇒ Complement of ∠A = 38°

Measure of ∠A = 90° – 38°

                          = 52°

Hence m∠A = 52°.

(8) Given complement of 27° = 90° – 27°

                                                 = 63°

Supplement of ∠B = Complement of 27°

⇒ Supplement of ∠B = 63°

Measure of ∠B = 180° – 63°

                          = 117°

Hence m∠B = 117°.

3 0
3 years ago
Student incorrectly claims that 2/3÷5/9 = 5/6 find the correct quotient what was the students error
olga_2 [115]

Answer:

6/5

Step-by-step explanation:

2/3 ÷ 5/9

2/3 × 9/5 ( while changing division to multiple, numerator and denominator changes

2 × 3/5 ( 9/3 =3

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Step-by-step explanation:

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Step-by-step explanation:

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