Answers
Answer:
(i) x = 17 cm
(ii) one end: 360 cm²; both ends: 720 cm²
(iii) 14,400 cm³
(iv) 4000 cm²
Step-by-step explanation:
You want the slant height, base area, volume, and total surface area of a trapezoidal prism with the base isosceles trapezoid having parallel base lengths of 32 and 16, and a height of 15. The distance between bases is 40. All units are cm.
(i) Slant heightIf a center rectangle 16 cm wide and 15 cm high is cut from the base trapezoid, the remaining two triangles have a base of 8 cm and a height of 15 cm. The Pythagorean theorem can be used to find the slant height:
x² = a² +b²
x² = 8² +15² = 64 +225 = 289
x = √289 = 17
The slant height, x, is 17 cm.
(ii) Base areaThe area of the base trapezoid is given by the formula ...
A = 1/2(b1 +b2)h
A = 1/2(32 +16)(15) = 360 . . . . square cm
The area of one end surface is 360 cm²; the total area of both end surfaces is 720 cm².
(iii) VolumeThe volume of the prism is the product of the base area and the length of the prism.
V = Bh
V = (360 cm²)(40 cm) = 14,400 cm³
The volume of the trapezoidal prism is 14,400 cm³.
(iv) Total surface areaThe lateral surface area of the prism is the product of the perimeter of the base and the distance between bases.
LA = Ph
LA = (32 +16 +2·17 cm)(40 cm) = 3280 cm²
The total surface area is the sum of the lateral area and the area of the two bases:
SA = LA +2B = (3280 cm²) + 2(360 cm²) = 4000 cm²
The total surface area of the prism is 4000 square centimeters.
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Additional comment
It appears that the top dashed line in the figure is drawn that way in error. It appears to identify a visible edge, so we expect it to be a solid line.
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Answers
Answer:
240/(v+40) + 1 > 240/v
Step-by-step explanation:
Both parties traveled a distance of 240 km.
Simpsons took off at average speed of 40 km/h & 1 hour later: 240/(v+40) + 1
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Answers
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Step-by-step explanation:
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Answer:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
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Answers
Answer:
Step-by-step explanation:
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Answers
Answer:
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Step-by-step explanation:
If a square has a perimeter of 16, then its side lengths are 4.
Use the pythagorean theorem to find the diagonal.
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Step-by-step explanation:
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Step-by-step explanation:
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Answers
Given right triangle ABC with altitude BD drawn to hypotenuse AC. If AB = 18
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A
D
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18
B
Answers
Answer:
8 is the length
Step-by-step explanation:
The length of AD is 9 units from the given right triangle ABC.
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Given right triangle ABC with altitude BD drawn to hypotenuse AC.
Given that, AB = 18 and AC = 36
Using Pythagoras theorem
AC²=AB²+BC²
⇒ 36²=18²+BC²
⇒ BC²=1296-324
⇒ BC²=972
⇒ BC=31.18 units
We know that, area of a triangle =1/2 × Base × Height
= 1/2 × 31.18 × 18
= 280.62 square units
Now, area of a triangle ABC with base AC and height BD
That is, Area = 1/2 ×36×BD
⇒ 18BD=280.62
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AB²=AD²+BD² (Pythagoras theorem)
18²=x²+15.6²
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Mr. Nguyen opened a savings account with an initial deposit of $480 and will not make any additional deposits or withdrawals. The account earns 2% simple interest. What is the total amount that Mr. Nguyen will have in his account at the end of 3 years?
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D $768.00
Answers
Answer:
c
Step-by-step explanation:
The next model of a sports car will cost 5.6% less than the current model. The current model costs $52,000. How much will the price decrease in dollars? What
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Answers
Answer:
49,088
Step-by-step explanation:
First you need to find 5.6% of 52,000. Simply multiply 52,000 by 0.056 (change the percent to a decimal) then you get 2,912.
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the temperature in Moscow was 2 degrees Celsius then it dropped to 8 degrees Celsius below zero by how many degrees did the temperature drop
Answers
Answer:
11
Step-by-step explanation:
2-8 you need to minus the first number
A camping store is having a summer sale. Stoves are being sold at 40% off. If the sale price is $57 what was the original price of the stove before the sale
Answers
Answer:
The original price was $142.5.
Step-by-step explanation:
40 ÷ 100 = 0.4
$57 ÷ 0.4 = $142.5
Therefore, $142.5 is our answer.
Answer:
142.5
Step-by-step explanation:
Let's say the original price of the store before the sale is x
so 40% x X = $57
40/100 (X ) =57
0.4 (X) = 57 ====> X = 57 / 0.4 = 142.5
The original price of the stove before the sale is $ 142.5