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3 years ago

PLEASE HELP ON THIS, Find the area of the shape shown below.

Mathematics

2 answers:

Bas_tet [7]3 years ago

7 0

Answer:

Area of the shape = 240 unit²

Step-by-step explanation:

Shape in the figure attached there are two parts. One is a triangle and other a rectangle.

By adding the area of these two shapes we can get the area of complete shape.

1). Area of the triangle = $\frac{1}{2}(base)(height)$

Base of the triangle = 20 units

height of the triangle = 4 units

Therefore area of triangle = $\frac{1}{2}(4)(20)=40$ square units

2). Area of rectangle = Length × width

= 20 × 10 = 200 unit²

Total area of the shape = area of triangle + area of rectangle

= 40 + 200 = 240 unit²

So the answer is area of the shape = 240 unit²

Arisa [49]3 years ago

7 0

240 units²

<h3>Further explanation</h3>

Given:

A rectangle with length = 20 units and width = 10 units.
Isosceles triangle with base = 20 units and height = 4 units.

Question:

Find the total area of the shape shown below.

The Process:

Step-1: find out the area of rectangular

The area = length x width

The area = 20 x 10

Hence, the area of rectangle is 200 units².

Step-2: find out the area of isosceles triangle

The area = $\frac{1}{2} \times base \times height$

The area = $\frac{1}{2} \times 20 \times 4$

The area = 10 x 4

Hence, the area of triangle is 40 units².

Step-3: find out the total area

Let us calculate the sum of the area of rectangles and triangles.

Total area = 200 units² + 40 units²

<em>Thus, the total area of the shape shown is 240 units².</em>

- - - - - - - - - -

Notes

If we want to calculate the total circumference, the length of the hypotenuse of the triangle must be determined through the Pythagorean Theorem.

<h3>Learn more</h3>

What is the area of triangle ABC brainly.com/question/4206319
Find out the area of a cube brainly.com/question/12613605
What is the area of gardening box? brainly.com/question/338448

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trapecia [35]

Answer:

Solution ( Second Attachment ) : - 2.017 + 0.656i

Solution ( First Attachment ) : 16.140 - 5.244i

Step-by-step explanation:

Second Attachment : The quotient of the two expressions would be the following,

$6\left[\cos \left(\frac{2\pi }{5}\right)+i\sin \left(\frac{2\pi \:}{5}\right)\right]$ ÷ $2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]$

So if we want to determine this expression in standard complex form, we can first convert it into trigonometric form, then apply trivial identities. Either that, or we can straight away apply the following identities and substitute,

( 1 ) cos(x) = sin(π / 2 - x)

( 2 ) sin(x) = cos(π / 2 - x)

If cos(x) = sin(π / 2 - x), then cos(2π / 5) = sin(π / 2 - 2π / 5) = sin(π / 10). Respectively sin(2π / 5) = cos(π / 2 - 2π / 5) = cos(π / 10). Let's simplify sin(π / 10) and cos(π / 10) with two more identities,

( 1 ) $\cos \left(\frac{x}{2}\right)=\sqrt{\frac{1+\cos \left(x\right)}{2}}$

( 2 ) $\sin \left(\frac{x}{2}\right)=\sqrt{\frac{1-\cos \left(x\right)}{2}}$

These two identities makes sin(π / 10) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , and cos(π / 10) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ .

Therefore cos(2π / 5) = $\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}$ , and sin(2π / 5) = $\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}$ . Substitute,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[\cos \left(\frac{-\pi }{2}\right)+i\sin \left(\frac{-\pi \:}{2}\right)\right]$

Remember that cos(- π / 2) = 0, and sin(- π / 2) = - 1. Substituting those values,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[0-i\right]$

And now simplify this expression to receive our answer,

$6\left[ \left\frac{\sqrt{2}\sqrt{3-\sqrt{5}}}{4}+i\left\frac{\sqrt{2}\sqrt{5+\sqrt{5}}}{4}\right]$ ÷ $2\sqrt{2}\left[0-i\right]$ = $-\frac{3\sqrt{5+\sqrt{5}}}{4}+\frac{3\sqrt{3-\sqrt{5}}}{4}i$ ,

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$6\sqrt{5+\sqrt{5}}-6i\sqrt{3-\sqrt{5}}$

We know that $6\sqrt{5+\sqrt{5}} = 16.13996\dots$ and $-\:6\sqrt{3-\sqrt{5}} = -5.24419\dots$ . Therefore,

Solution : $16.13996 - 5.24419i$

Which rounds to about option b.

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