Question

Бісектриса АМ паралелограма ABCD ділить сторону ВС на відрізки ВМ = 10 см, МС= 8 см. Знайдіть площу паралелограма, якщо A=30°. СРОЧНОО!!!! ДАЮ 35 БАЛОВ

Answer 1

Решение в приложении.

Answer 2

Bisector of AM in parallelogram ABCD

To find the area of parallelogram ABCD, we need to use the given information about the bisector of AM and the measurements of VM and MS.

Let's break down the problem step by step:

1. We are given that the bisector of AM divides side BC into two segments, VM and MS. We are also given that VM = 10 cm and MS = 8 cm.

2. We are told that angle A is 30°.

To find the area of parallelogram ABCD, we can use the formula:

Area = base × height

In a parallelogram, any side can be considered as the base. Let's consider side BC as the base.

To find the height, we need to determine the perpendicular distance between side BC and point A. Let's call this distance h.

To find h, we can use the formula:

h = VM × sin(A)

where VM is the length of segment VM and A is the angle between side BC and the bisector of AM.

Let's substitute the given values into the formula:

h = 10 cm × sin(30°)

Using a calculator, we find that sin(30°) = 0.5. Therefore:

h = 10 cm × 0.5 = 5 cm

Now that we have the height, we can calculate the area of parallelogram ABCD:

Area = BC × h

Since BC is the base, we need to find its length. BC is equal to the sum of VM and MS:

BC = VM + MS = 10 cm + 8 cm = 18 cm

Substituting the values into the formula:

Area = 18 cm × 5 cm = 90 cm²

Therefore, the area of parallelogram ABCD is 90 square centimeters.

Please note that the above solution is based on the information provided in the question. If there are any additional constraints or information, please let me know, and I'll be happy to assist you further.