ABCD is a retangle of perimeter 48cm with AB =6cm and CD = DE what is the area of rectangular ofACE?
Where the heck is point E?
All we know is that it lies on a circle of radius 6 with center at D.
And ACE is not a rectangle!
Fix your question, and then maybe you can expect some help. SMH
To find the area of rectangle ACE, we need to determine the length of AC and CE.
Given:
Perimeter of the rectangle = 48 cm
AB = 6 cm
CD = DE
The perimeter of a rectangle is given by the formula:
Perimeter = 2 × (Length + Width)
Since AB = CD, we know that AB = CD = 6 cm.
Let's set up an equation using the given information:
48 = 2 × (AC + BC)
We know that BC = CD = DE = 6 cm, so the equation becomes:
48 = 2 × (AC + 6)
Dividing both sides of the equation by 2, we have:
24 = AC + 6
Subtracting 6 from both sides, we get:
AC = 18
Now, we can calculate the area of rectangle ACE:
Area = Length × Width
Area = AC × CE
Since we know AC = 18 cm, we need to determine CE.
Since AB = CD = DE, we know that BC = CD = DE = 6 cm.
Since ABCD is a rectangle, AC is parallel to BD. Therefore, the length of BD is 18 cm.
Since BCE is a right-angled triangle, we can use Pythagoras' theorem to find CE.
Pythagoras' theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In triangle BCE, BC is the base, CE is the height, and BD is the hypotenuse.
Let's use Pythagoras' theorem:
BD^2 = BC^2 + CE^2
18^2 = 6^2 + CE^2
324 = 36 + CE^2
CE^2 = 324 - 36
CE^2 = 288
Taking the square root of both sides, we have:
CE = √288 = 16.97 cm (rounded to two decimal places)
Now, we can calculate the area of rectangle ACE:
Area = AC × CE
Area = 18 cm × 16.97 cm = 305.46 cm^2 (rounded to two decimal places)
Therefore, the area of rectangle ACE is approximately 305.46 cm^2.