The area of the kite can be calculated by multiplying the lengths of the diagonals and dividing this product by .
The area of the kite can be calculated by multiplying the lengths of the diagonals and dividing this product by .
To facilitate the understanding of the concept of calculus, you can use the following drawing and the accompanying formula:
Look at the kite ABCD below.
Diagonal DB = 10
CB = 4
Is it possible to calculate the area of the kite? If so, what is it?
There are many geometric shapes that can be found during the solving of engineering problems at all different stages of study, such as in high school, in matriculation exams, and even in psychometry. One of the less trivial shapes is the deltoid and, as part of the questions surrounding it, students are often asked to calculate the area of the deltoid.
A deltoid is a polygon with four sides (that is, a quadrilateral) with two distinct sets of adjacent sides of equal length to each other.
Given the deltoid ABCD
Find the area
Given the deltoid ABCD
Find the area
Given the deltoid ABCD
Find the area
There is a clear distinction between convex deltoid and concave deltoid.
Convex deltoid is a deltoid where the diagonals are inside and cross each other. The longer diagonal acts as a main diagonal, while the shorter diagonal acts as a secondary diagonal.
As you can observe in the following drawing, the main diagonal divides the deltoid into two overlapping triangles, that is, identical, and the secondary diagonal divides the deltoid into two isosceles triangles whose bases are adjacent and, indeed, identical.
Given the deltoid ABCD
Find the area
Given the deltoid ABCD
Find the area
Given the deltoid ABCD
Find the area
Concave kite is a kite where one of the diagonals (main diagonal) passes inside the kite and the other diagonal (secondary diagonal) passes outside the kite.
The concave deltoid can be described as a shape consisting of two isosceles triangles that share a common base, where one triangle contains the other triangle. The following drawing better describes the concave deltoid:
Given the deltoid ABCD
Find the area
Given the deltoid ABCD
Find the area
Given the deltoid ABCD
Find the area
Given the kite whose area is cm², the meeting point of the diagonals and .
The area of the section KP must be calculated according to the attached drawing and the existing data:
Solution:
This exercise is a reverse calculation, that is, we know the area and we are asked to calculate the length of the segment .
In the first step, we replace the data we know in the kite area formula.
We obtain:
We simplify the expression and obtain:
In fact, we found the length of the second diagonal of the kite.
According to one of the properties of the kite, the diagonal divides the diagonal into two equal parts.
From here we obtain that is equal to cm.
Answer:
cm
Look at the kite ABCD below.
Diagonal DB = 10
CB = 4
Is it possible to calculate the area of the kite? If so, what is it?
To determine if we can calculate the area of the kite, let's consider the steps we would use given complete data:
To calculate the area of a kite, we typically use the formula:
where and represent the lengths of the kite's diagonals.
In this case:
Without knowing , we cannot apply the formula to calculate the area. Thus, given the information provided, it is not possible to determine the area of the kite.
Therefore, the solution to the problem is: It is not possible.
It is not possible.
Given the deltoid ABCD
Find the area
To find the area of deltoid , we will use the known formula for the area of a deltoid based on its diagonals. Let's perform the calculation step-by-step:
Thus, the area of deltoid is cm².
cm².
Given the deltoid ABCD
Find the area
To solve this problem, we need to calculate the area of the deltoid using the given lengths of its diagonals. The formula for the area of a deltoid (kite) is:
Where and are the lengths of the diagonals. From the diagram, we know:
Substituting these values into the formula, we have:
Calculating this gives:
Therefore, the area of the deltoid is cm².
The correct answer from the given choices is:
cm².
cm².
Given the deltoid ABCD
Find the area
To solve the problem of finding the area of the deltoid (kite) ABCD, we will apply the formula for the area of a kite involving its diagonals:
The formula is:
Where and are the lengths of the diagonals. From the problem’s illustration:
The image references imply through markings that their impact in shape is demonstrated via convergence of matching altitudes and isos of plot. The diagonal proportion can be referred via an intercept mark mutual to setup if not altered by mistake redundantly.
Thus: Calculated area
The calculated area matches with the choice option:
Therefore, the area of the deltoid is .
cm².
Given the deltoid ABCD
Find the area
To solve this problem, we need to calculate the area of the deltoid using the formula for the area in terms of diagonals:
Thus, the area of the deltoid is .
Therefore, the solution to the problem is , which corresponds to choice 3.
cm².
Given the deltoid ABCD
Find the area
Indicate the correct answer
The next quadrilateral is:
Indicate the correct answer
The next quadrilateral is: