Triangle ADE is inside rectangle ABCD. Point E is half way between points B and C on the rectangle. Since AB is 8 cm and side AD is 7 cm.
1. what is the area of triangle ADE?
2. what is the ratio of the area of the triangle ABE to the area of triangle ADE?
3. What is the ratio of the area of the triangle CDE to the area of rectangle ABCD?
Thanks so much!!!
1. area = (1/2)(8)(7) = 28
2. triangle ABE : triangle ADE = 1 : 2
3. area CDE : rect ABCD = 1 : 4
thx so much!!!
To solve the given questions, we can use the properties of similar triangles and basic geometry formulas.
1. Area of Triangle ADE:
Since AB is 8 cm and AD is 7 cm, we can use the formula for the area of a triangle: Area = 1/2 * base * height.
The base of Triangle ADE is AD, which is 7 cm.
To find the height, we draw a line connecting point E to side AD (let's call this line EF).
Since point E is halfway between points B and C on the rectangle, we can assume EF is equal to half the length of BC. Therefore, EF = 1/2 * BC.
BC is equal to AB, which is 8 cm.
So, EF = 1/2 * 8 cm = 4 cm.
The height of Triangle ADE is then 4 cm.
Using the formula for the area of a triangle, we can calculate the area of Triangle ADE:
Area_ADE = 1/2 * AD * EF = 1/2 * 7 cm * 4 cm = 14 cm^2.
Therefore, the area of Triangle ADE is 14 cm^2.
2. Ratio of Area of Triangle ABE to Area of Triangle ADE:
To find the ratio, we need to calculate the areas of Triangle ABE and Triangle ADE.
Since Triangle ABE and Triangle ADE share the same base (AD), the ratio of their areas will be equal to the ratio of their heights.
The height of Triangle ABE is EF, which we calculated earlier as 4 cm.
Therefore, the ratio of the area of Triangle ABE to the area of Triangle ADE is 4:14, which simplifies to 2:7.
3. Ratio of Area of Triangle CDE to the Area of Rectangle ABCD:
To find the ratio, we need to calculate the areas of Triangle CDE and Rectangle ABCD.
The area of Triangle CDE can be found using the same formula as in step 1:
The base of Triangle CDE is CD, which is equal to AB, 8 cm.
The height of Triangle CDE is EF, 4 cm.
Using the formula for the area of a triangle:
Area_CDE = 1/2 * CD * EF = 1/2 * 8 cm * 4 cm = 16 cm^2.
The area of Rectangle ABCD can be found by multiplying its length AB by its width BC:
Area_ABCD = AB * BC = 8 cm * 8 cm = 64 cm^2.
Therefore, the ratio of the area of Triangle CDE to the area of Rectangle ABCD is 16:64, which simplifies to 1:4.
To find the answers to the given questions, we can use the properties of triangles and rectangles. Let's break down each question step by step:
1. Area of Triangle ADE:
To find the area of triangle ADE, we need to know the length of its base and its height. In this case, the base AD has a length of 7 cm. To find the height, we can use the fact that point E is halfway between points B and C.
Since AB is 8 cm, and E is halfway between B and C, the length of BE would be half of AB, which is 8/2 = 4 cm. Since E lies on AD, DE would also have a length of 4 cm.
Now we have the base AD = 7 cm and the height DE = 4 cm. The area of a triangle is given by the formula 1/2 * base * height. Therefore, the area of triangle ADE = 1/2 * 7 cm * 4 cm = 14 cm².
2. Ratio of the area of Triangle ABE to Triangle ADE:
To find this ratio, we need to calculate the areas of both triangles ABE and ADE. We know that the base of both triangles is 7 cm, as it is the same as the base of triangle ADE.
The height of triangle ABE is the same as DE, which is 4 cm. Therefore, the height of triangle ABE is also 4 cm.
The area of triangle ABE is given by the formula 1/2 * base * height. Therefore, the area of triangle ABE = 1/2 * 7 cm * 4 cm = 14 cm².
Now we can find the ratio of the areas by dividing the area of triangle ABE by the area of triangle ADE. So, the ratio is 14 cm² : 14 cm², which simplifies to 1 : 1.
3. Ratio of the area of Triangle CDE to Rectangle ABCD:
To find this ratio, we need to calculate the areas of both triangle CDE and rectangle ABCD.
The area of triangle CDE is given by the formula 1/2 * base * height. The base CD is the same length as AD, which is 7 cm. The height DE is 4 cm. Therefore, the area of triangle CDE = 1/2 * 7 cm * 4 cm = 14 cm².
The area of rectangle ABCD is given by the formula length * width. The length AB is 8 cm, and the width BC is also 8 cm, as it is opposite to AB. Therefore, the area of rectangle ABCD = 8 cm * 8 cm = 64 cm².
Now we can find the ratio of the areas by dividing the area of triangle CDE by the area of rectangle ABCD. So, the ratio is 14 cm² : 64 cm², which simplifies to 7 : 32.
To summarize:
1. The area of triangle ADE is 14 cm².
2. The ratio of the area of triangle ABE to triangle ADE is 1 : 1.
3. The ratio of the area of triangle CDE to rectangle ABCD is 7 : 32.