All categories

2 years ago

What is the area of the figure below a. 7.5 b. 15 c. 21.25 d. 42.5

Mathematics

2 answers:

weeeeeb [17]2 years ago

7 0

Answer:

The correct answer is option C. 21.25

Step-by-step explanation:

Formula:-

Area of triangle = bh/2

Where b - Base of triangle and h - Height of triangle

From the figure we can see a two isosceles triangle.

One triangle with base 5 m(2.5 + 2.5) and height 2.5 m

The second triangle with base 5 m and height 6

To find the area of first triangle

Here b = 5 m and h = 2.5 m

Area = bh/2 =(5 * 2.5)/2 = 6.25 m²

To find the area of second triangle

Here b = 5 m and h = 6 m

Area = bh/2 =(5 * 6)/2 = 15 m²

To find total area 

Total area = Area of 1st triangle + area of 2nd triangle

= 6.25 + 15 = 21.25 m²

The correct answer is option C. 21.25

Marina86 [1]2 years ago

6 0

Check the picture below.

let's recall that in a Kite, the diagonals meet at 90° angles, therefore, we know the height of each of those 4 triangles, is 2.5 and 6, now, since the pair of triangles above are 45-45-90 triangles, we can use the 45-45-90 rule, as you see there, so, if the height is 2.5, then the base is also 2.5.

so, we really have 2 pair of triangles whose base is 2.5 and height of 2.5, and another pair of triangles whose base is 2.5 and height is 6, let's add their areas.

$\bf \stackrel{\textit{area of 2 triangles above}}{2\left[\cfrac{1}{2}(2.5)(2.5) \right]}~~+~~\stackrel{\textit{area of 2 triangles below}}{2\left[ \cfrac{1}{2}(2.5)(6) \right]}\implies 6.25+15\implies 21.25$

You might be interested in

Suppose that v is an eigenvector of matrix A with eigenvalue λA, and it is also an eigenvector of matrix B with eigenvalue λB. (

galben [10]

Answer:

(a) Yes, $λ_{A}+λ_{B}$

(b) Yes, $λ_{A}λ_{B}$

Step-by-step explanation:

First, lets understand what are eigenvectors and eigenvalues?

Note: I am using the notation $λ_{A}$ to denote Lambda(A) sign.

$v$ is an eigenvector of matrix A with eigenvalue $λ_{A}$

$v$ is also eigenvector of matrix B with eigenvalue $λ_{B}$

So we can write this in equation form as

$Av=λ_{A}v$

So what does this equation say?

When you multiply any vector by A they do change their direction. any vector that is in the same direction as of $Av$ , then this $v$ is called the eigenvector of $A$ . $Av$ is $λ_{A}$ times the original $v$ . The number $λ_{A}$ is the eigenvalue of A.

$λ_{A}$ this number is very important and tells us what is happening when we multiply $Av$ . Is it shrinking or expanding or reversed or something else?

It tells us everything we need to know!

Bonus:

By the way you can find out the eigenvalue of $Av$ by using the following equation:

$det(A-λI)=0$