Question

finding area using congruent rectangles
rectangle abcd is congruent to rectangle hgjk.
what is the area of rectangle abcd?
k 18 in. h
a 11 in. b
j g
d c
square inches

Explanation:

Step1: Recall congruent rectangles property

Congruent rectangles have equal length and width. So, rectangle \(ABCD\) and \(HGJK\) have same dimensions.

Step2: Identify length and width of \(ABCD\)

From the diagram, length of \(AB = 11\) in (same as corresponding side of \(HGJK\)'s width? Wait, no—wait, congruent rectangles: so the length of \(HGJK\) is \(18\) in, and the length of \(AB\) is \(11\) in? Wait, no, wait: congruent rectangles have corresponding sides equal. So, if \(ABCD\) is congruent to \(HGJK\), then the length of \(ABCD\) is equal to the length of \(HGJK\) (or width, depending on orientation), and width equal. Wait, looking at the rectangles: \(ABCD\) has \(AB = 11\) in (let's say that's the width), and \(HGJK\) has \(KH = 18\) in (length). Since they are congruent, the length of \(ABCD\) is \(18\) in and width is \(11\) in.

Step3: Calculate area of rectangle

Area of a rectangle is \( \text{length} \times \text{width} \). So, for \(ABCD\), length \( = 18\) in, width \( = 11\) in. So area \( = 18 \times 11 \).
Calculating \(18 \times 11\): \(18\times10 = 180\), \(18\times1 = 18\), so \(180 + 18 = 198\).

Answer:

198