Question

A greeting card uses a geometric design containing 4 congruent kites. The card is 4 inches wide and 8 inches long. What is the area of one kite? 4 sq. in. 8 sq. in. 12 sq. in. 16 sq. in.

Answer 1

Answer:

4 square inches

Step-by-step explanation:

Refer the attached figure .

Since the card is 8 inches long .

So, length of Vertical diagonal of 1 kite + length of Vertical diagonal of another kite = 8

Since we are given that the kites are congruent

So, length of Vertical diagonal of both kites will be same

So, 2 (length of Vertical diagonal of 1 kite ) = 8

So, length of Vertical diagonal of 1 kite = 4 inches

Now width of card is 4 inches

So, length of Horizontal diagonal of 1 kite + length of Horizontal diagonal of another kite =4

Since we are given that the kites are congruent

So, length of Horizontal diagonal of both kites will be same

So, 2 (length of Horizontal diagonal of 1 kite ) = 4

So, length of Horizontal diagonal of 1 kite = 2 inches

So length of vertical diagonal of kite is 4 inches and horizontal diagonal is 2 inches

So, Area of kite = $\frac{pq}{2}$

Where p and q are the diagonals of kite

Area of kite = $\frac{4 \times 2}{2}$

                   = $4 inches^2$

Hence the area of one kite is 4 sq. inches.

Answer 2

The area of the one kite is 4 square inches if the greeting card uses a geometric design containing 4 congruent kites and the card is 4 inches wide and 8 inches long, an option first is correct.

What is quadrilateral?

It is defined as the four-sided polygon in geometry having four edges and four corners. KIte is a quadrilateral having two pairs of congruent sides and It has one pair of opposite congruent angles. The diagonals of a kite are perpendicular.

We have:

A greeting card uses a geometric design containing 4 congruent kites.

The card is 4 inches wide and 8 inches long.

As the kites are congruent;

2(length of the vertical diagonal of one kite) = 8

Let's suppose the length of the vertical diagonal of one kite is p

2p = 8

p = 4 in

2(length of the horizontal diagonal of one kite) = 4

Let's suppose the length of the horizontal diagonal of one kite is q

2q = 4

q = 2

Now, the area of the kite is given by:

$\rm A = \frac{pq}{2}$

$\rm A = \frac{4\times2}{2}$

A = 4 square in.

Thus, the area of the one kite is 4 square inches if the greeting card uses a geometric design containing 4 congruent kites and the card is 4 inches wide and 8 inches long, an option first is correct.

Learn more about the quadrilateral here:

brainly.com/question/6321910

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