Question

The garden is made up of a rectangular patch of grass and two semi-circular vegetable patches. If the dimensions of the rectangular patch are 16 m (length) and 8 m (width) respectively, calculate: a) the perimeter of the garden. b) the total area of the garden.

Performing transformations
ANSWERED
asked 2020-10-18
The garden is made up of a rectangular patch of grass and two semi-circular vegetable patches. If the dimensions of the rectangular patch are 16 m (length) and 8 m (width) respectively, calculate: a) the perimeter of the garden.
b) the total area of the garden.

Answers (1)

2020-10-19
a)The perimeter consists of the two lengths of the rectangle (16 m) and the two curve sides of the semicircles whose radius is half the width of the rectangle or \(\displaystyle\frac{{1}}{{2}}{\left({8}\right)}={4}\). Hence,
\(\displaystyle{P}={2}{l}+{2}{\left(\frac{{1}}{{2}}\right)}{\left({2}π{r}\right)}\)
\(\displaystyle{P}={2}{\left({16}\right)}+{2}{\left(\frac{{1}}{{2}}\right)}{\left({2}π\cdot{4}\right)}\)
\(\displaystyle{P}={32}+{8}π\sim{57.1}{m}\)
b)The total area is the area of the rectangle plus the areas of the semicircles:
\(\displaystyle{A}={l}{w}+{2}{\left(\frac{{1}}{{2}}\right)}π{r}^{{2}}\)
\(\displaystyle{A}={\left({16}\right)}{\left({8}\right)}+{2}{\left(\frac{{1}}{{2}}\right)}π{\left({4}\right)}^{{2}}\)
\(\displaystyle{A}={128}+{16}π\sim{178.3}{m}^{{2}}\)
0
 
Best answer

expert advice

Need a better answer?

Relevant Questions

asked 2020-10-26
The ratio of the length (including the endzone) to the width of an NFL football field is 2.25. If the perimeter of the football field is 1040 feet, what are the dimensions of the field?
asked 2021-05-03
A rectangular swimming pool is three times as long as it is wide. If the perimeter of the pool is 320 feet, what are its dimensions?
asked 2021-03-30
A long, straight, copper wire with a circular cross-sectional area of \(\displaystyle{2.1}{m}{m}^{{2}}\) carries a current of 16 A. The resistivity of the material is \(\displaystyle{2.0}\times{10}^{{-{8}}}\) Om.
a) What is the uniform electric field in the material?
b) If the current is changing at the rate of 4000 A/s, at whatrate is the electric field in the material changing?
c) What is the displacement current density in the material in part (b)?
d) If the current is changing as in part (b), what is the magnitude of the magnetic field 6.0cm from the center of the wire? Note that both the conduction current and the displacement currentshould be included in the calculation of B. Is the contribution from the displacement current significant?
asked 2021-05-22
Sheila is in Ms. Cai's class . She noticed that the graph of the perimeter for the "dented square" in problem 3-61 was a line . "I wonder what the graph of its area looks like ," she said to her teammates .
a. Write an equation for the area of the "dented square" if xx represents the length of the large square and yy represents the area of the square.
b. On graph paper , graph the rule you found for the area in part (a). Why does a 1st−quadrant graph make sense for this situation? Are there other values of xx that cannot work in this situation? Be sure to include an indication of this on your graph, as necessary.
c. Explain to Sheila what the graph of the area looks like.
d. Use the graph to approximate xx when the area of the shape is 20 square units.
...