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3 years ago

Find the area of the figure

Mathematics

2 answers:

kondaur [170]3 years ago

6 0

Answer:

22.23 yd²

Step-by-step explanation:

The figure is a trapezium and area can be calculated using the formula

A = $\frac{1}{2}$ h(a + b)

where h is the height and a, b the parallel bases

here h = 5.7, a = 5.9 and b = 1.9

A= 0.5 × 5.7(5.9 + 1.9) = 0.5 × 5.7 × 7.8 = 22.23 yd²

GREYUIT [131]3 years ago

5 0

Answer:

22.3 is the answer

$\frac{a+b}{2}*h$ = $\frac{1.9+5.9}{2} *5.7 = \frac{7.8}{2} * 5.7 = 3.9 * 5.7 = 22.23$

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Answer:

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The series are given as geometric series because these terms have common ratio and not common difference.

Our common ratio is 2 because:

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The summation formula for geometric series (r ≠ 1) is:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}$ or $\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

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$\displaystyle \large{S_5=\frac{1(2^5-1)}{2-1}}\\\displaystyle \large{S_5=\frac{2^5-1}{1}}\\\displaystyle \large{S_5=2^5-1}\\\displaystyle \large{S_5=32-1}\\\displaystyle \large{S_5=31}$

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Summary

If the sequence has common ratio then the sequence or series is classified as geometric sequence/series.

Common Ratio can be found by either multiplying terms with common ratio to get the exact next sequence which can be expressed as $\displaystyle \large{a_{n-1} \cdot r = a_n}$ meaning “previous term times ratio = next term” or you can also get the next term to divide with previous term which can be expressed as:

$\displaystyle \large{r=\frac{a_{n+1}}{a_n}}$

Once knowing which sequence or series is it, apply an appropriate formula for the series. For geometric series, apply the following three formulas:

$\displaystyle \large{S_n=\frac{a_1(r^n-1)}{r-1}}\\\displaystyle \large{S_n=\frac{a_1(1-r^n)}{1-r}}$

Above should be applied for series that have common ratio not equal to 1.

$\displaystyle \large{S_n=a_1 \cdot n}$

Above should be applied for series that have common ratio exactly equal to 1.

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Topics

Sequence & Series — Geometric Series

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Others

Let me know if you have any doubts about my answer, explanation or this question through comment!

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Find the area of the figure ​

Find the area of the figure