A large square is divided into 4 smaller squares; then small left square is divided into 4 smaller squares as well. What fraction of the large square is
shaded?

OPTIONS

4 over 5
3 over 8
4 over 9
1 over 3
1 over 2​

The total fraction shaded is 1/2

Step-by-step explanation:

Here, we want to know the fraction shaded

As we can see, the box is originally divided into 4

So each of the 4 parts are 1/4

for the first part, we have 4 divisions;

This means each of the divisions with respect to the whole fraction will be 1/4/4 = 1/16

Now, two of these are shaded, making 1/16 and 1/16

Secondly, we have half of the 1/4 : So with respect to the whole, we have 1/4/2 = 1/8

for the third part, the whole 1/4 is shaded

and lastly, we have an unshaded 1/4

so, the total fraction shaded will be ;

1/16 + 1/16 + 1/4 + 1/8

= (1 + 1 + 4 + 2)/16 = 8/16 = 1/2

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)