Point A,B,C and D are midpoints of sides of square EFGH. If area of EFGH is 48cm2 then area of ABCD is? (ans 24cm2)
if you draw the diagram, you can see that the sides of ABCD are the hypotenuses of triangles formed at the corners of EFGH. So, the sides of ABCD are 1/√2 as long as the sides of EFGH.
So, the area of ABCD is 1/2 the area of EFGH: 24 cm^2
To find the area of the smaller square ABCD, we can use the relationship between the areas of similar figures.
Given that A, B, C, and D are midpoints of the sides of square EFGH, it means that each side of ABCD is half the length of each side of EFGH.
Let's assume the length of each side of EFGH is x. Therefore, the area of EFGH is (x^2).
Since A, B, C, and D are midpoints of the sides, the length of each side of ABCD is x/2. Therefore, the area of ABCD is ((x/2)^2) = (x^2)/4.
We are given that the area of EFGH is 48 cm^2. So, we can set up the equation:
(x^2) = 48
To solve for x, we can take the square root of both sides of the equation:
x = √48
Now, we can substitute the value of x into the equation for the area of ABCD:
Area of ABCD = (x^2)/4 = ((√48)^2)/4
Simplifying further:
Area of ABCD = (48/4) = 12 cm^2
Therefore, the area of square ABCD is 12 cm^2, not 24 cm^2 as stated in the given answer.