Question

Через середину діагоналі BD прямокутного АВСD проведено пряму ,яка перетинає сторони ВС і АD прямокутника в точках М і К відповідно,ВD=10см,МВ=6см,МС=2см.Обчисліть площу чотирикутника АМСК. Будь ласка допоможіть,дуже потрібно..........

Answer 1

BC=AD=BM+MC=6+2=8см
AB=√(BD²-AD²)=√(100-64)=√36=6см-высота ABCD  ANCK
MC=AK=2см
S(AMCK)=AK*AB=2*6=12см²

Answer 2

Finding the Length of AK:

To find the length of AK, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

Let's denote the length of AK as x. Then, we have the following equation: x^2 = (MD)^2 + (MK)^2

Given that MD = 10 cm, MK = 6 cm, and MC = 2 cm, we can calculate the length of AK using the Pythagorean theorem.

Calculating the Length of AK:

Using the Pythagorean theorem, we can calculate the length of AK as follows: x^2 = (10)^2 + (6)^2 x^2 = 100 + 36 x^2 = 136 x ≈ √136 x ≈ 11.66 cm

So, the length of AK is approximately 11.66 cm.

Calculating the Area of Quadrilateral AMSK:

To calculate the area of quadrilateral AMSK, we can use the formula for the area of a trapezoid, which is given by the formula: Area = (1/2) * (sum of parallel sides) * (distance between them)

In this case, the sides of the trapezoid are AM and KS, and the distance between them is AK. We already know the length of AK, which is approximately 11.66 cm. We also need to find the lengths of AM and KS.

Finding the Length of AM:

To find the length of AM, we can use the Pythagorean theorem again. Let's denote the length of AM as y. Then, we have the following equation: y^2 = (MD)^2 + (MA)^2

Given that MD = 10 cm and MC = 2 cm, we can calculate the length of AM using the Pythagorean theorem.

Calculating the Length of AM:

Using the Pythagorean theorem, we can calculate the length of AM as follows: y^2 = (10)^2 + (2)^2 y^2 = 100 + 4 y^2 = 104 y ≈ √104 y ≈ 10.20 cm

So, the length of AM is approximately 10.20 cm.

Finding the Length of KS:

To find the length of KS, we can use the fact that KS = AM, as opposite sides of a rectangle are equal.

Calculating the Area of Quadrilateral AMSK:

Now that we have the lengths of AK, AM, and KS, we can calculate the area of quadrilateral AMSK using the formula for the area of a trapezoid: Area = (1/2) * (AM + KS) * AK

Substituting the values we have found: Area = (1/2) * (10.20 + 10.20) * 11.66 Area ≈ (1/2) * 20.40 * 11.66 Area ≈ 119.16 cm^2

So, the area of quadrilateral AMSK is approximately 119.16 cm^2.