Question

Rectangle abcd is congruent to rectangle hgjk. What is the area of rectangle abcd? square inches.

Answer 1

Final answer:

To find the area of rectangle ABCD, one must know the specific dimensions of the rectangle. For squares, if the side length is doubled, the area becomes four times larger, as seen in the example with Marta's squares.

Step-by-step explanation:

The area of a rectangle or square is calculated by multiplying its length by its width. To determine the area of rectangle ABCD, we need to know its dimensions, which are not provided in the question. However, we can explore the concept of area using a related example involving squares.

Marta has an original square with a side length of 4 inches. The area of this square is found by squaring the side length: 4 inches × 4 inches = 16 square inches. If the side length of a similar square is doubled, the new side length is 8 inches (4 inches × 2). The area of the larger square is then 8 inches × 8 inches = 64 square inches.

To compare the areas, we use a ratio. The area of the larger square is four times the area of the smaller square (64 square inches : 16 square inches = 4:1). Hence, when the side length of a square is doubled, its area increases by a factor of four.

The complete question is: Rectangle abcd is congruent to rectangle hgjk. What is the area of rectangle abcd? square inches. is:

Answer 2

The area of rectangle ABCD is 198 square inches.

The image shows two rectangles, ABCD and HGJK. Rectangle ABCD is congruent to rectangle HGJK, meaning both rectangles have the same dimensions. The length of HGJK is given as 18 inches, and since ABCD is congruent to HGJK, it must have the same length. However, the width of ABCD is not directly given but it's indicated that AB is 11 inches, which would be the width of rectangle ABCD, as congruent rectangles have corresponding sides of equal length.

To find the area of rectangle ABCD, we use the formula:

`\[ \text{Area} = \text{length} * \text{width} \]`

From the image, we have:

- Length of ABCD (congruent to HG or JK) = 18 inches

- Width of ABCD (AB) = 11 inches

Now we can calculate the area:

`\[ \text{Area} = 18 \text{ inches} * 11 \text{ inches} \]`

`\[ \text{Area} = 198 \text{ square inches} \]`

So, the area of rectangle ABCD is 198 square inches.