Help me please. Find the area of the compound Shape

Mathematics

1 answer:

Setler79 [48]2 years ago

8 0

Hi there!

We can divide this shape into 3 rectangles.

1st rectangle dimensions: 5m × 3m

2nd rectangle: 12m × 4m

3rd rectangle: 2m × 5m

Find the areas using the equation:

A = l × w

1st rectangle: 5 × 3 = 15m²

2nd rectangle: 12 × 4 = 48m²

3rd rectangle: 2 × 5 = 10m²

Add the areas up:

15 + 48 + 10 = 73m²

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A geometric series has second term 375 and fifth term 81 . find the sum to infinity of series .

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Answer: $\bold{S_{\infty}=\dfrac{3125}{2}=1562.5}$

Step-by-step explanation:

a₁, 375, a₃, a₄, 81

First, let's find the ratio (r). There are three multiple from 375 to 81.

$375r^3=81\\\\r^3=\dfrac{81}{375}\\\\\\r^3=\dfrac{27}{125}\qquad \leftarrow simplied\\\\\\\sqrt[3]{r^3} =\sqrt[3]{\dfrac{27}{125}}\\ \\\\r=\dfrac{3}{5}$

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Lastly, Use the Infinite Geometric Sum Formula to find the sum:

$S_{\infty}=\dfrac{a_1}{1-r}\\\\\\.\quad =\dfrac{625}{1-\frac{3}{5}}\\\\\\.\quad =\dfrac{625}{\frac{2}{5}}\\\\\\.\quad = \dfrac{625(5)}{2}\\\\\\.\quad = \large\boxed{\dfrac{3125}{2}}$