Question

use the given information to answer each question. explain your reasoning.
sample problem
tommy drew a quadrilateral. he used a protractor to measure all four angles of the quadrilateral.
how many pairs of angles must be congruent for the quadrilateral to be a parallelogram?
in a parallelogram, opposite angles are congruent, so both pairs of opposite angles must be congruent.

alice created a kite out of two sticks and some fabric. the sticks were 10 inches and 15 inches long. she tied the sticks together so they were perpendicular and attached the fabric. when she measured the kite, she noticed that the distance from where the sticks meet to the top of the kite was 5 inches.
what is the area of the kite alice created?
enter the answer in the space provided. use numbers in square inches

Explanation:

Step1: Recall the area formula for a kite

A kite with diagonals \(d_1\) and \(d_2\) has an area \(A=\frac{1}{2}d_1d_2\). Here, the two sticks are the diagonals? Wait, no, the sticks are perpendicular, and the distance from the intersection to the top is 5 inches. Wait, the sticks are 10 and 15 inches? Wait, no, let's re - read. Alice's kite: two sticks, 10 inches and 15 inches long, perpendicular. Then the distance from where sticks meet to the top is 5 inches. Wait, maybe the diagonals are: one diagonal is 10 inches (or 15 inches) and the other is split? Wait, no, a kite has two pairs of adjacent sides equal, and the diagonals are perpendicular. The area of a kite is \(\frac{1}{2}\times\) product of the diagonals. Wait, maybe the two sticks are the diagonals? Wait, no, the sticks are perpendicular, so let's assume that the two diagonals are \(d_1\) and \(d_2\). Wait, the problem says "two sticks and some fabric. The sticks were 10 inches and 15 inches long. She tied the sticks together so they were perpendicular and attached the fabric. When she measured the kite, she noticed that the distance from where the sticks meet to the top of the kite was 5 inches." Wait, maybe one diagonal is 10 inches, and the other diagonal: the distance from the intersection to the top is 5 inches, so the total length of that diagonal is \(5 + x\), but wait, no, maybe the two sticks are the diagonals. Wait, no, let's think again. The area of a kite is \(\frac{1}{2}\times d_1\times d_2\), where \(d_1\) and \(d_2\) are the lengths of the two diagonals. If the two sticks are perpendicular, they are the diagonals. Wait, but then the distance from the intersection to the top is 5 inches. Wait, maybe one diagonal is 10 inches, and the other diagonal: the part from the intersection to the top is 5 inches, so the other part (from intersection to bottom) is, say, \(y\), but maybe the total length of the other diagonal is \(5 + y\), but we don't know \(y\). Wait, no, maybe I misread. Wait, the sticks are 10 and 15 inches, perpendicular. So the diagonals are 10 and 15 inches? Then the area would be \(\frac{1}{2}\times10\times15 = 75\)? But the distance from the intersection to the top is 5 inches. Wait, maybe one diagonal is 10 inches, and the other diagonal: the distance from the intersection to the top is 5 inches, so the length of that diagonal is \(5\times2=10\)? No, that doesn't make sense. Wait, maybe the two sticks are the diagonals, with lengths 10 and 15, and they are perpendicular. Then the area of the kite (which is a type of quadrilateral with perpendicular diagonals) is \(\frac{1}{2}\times10\times15\).

Step2: Calculate the area

Using the formula \(A = \frac{1}{2}d_1d_2\), where \(d_1 = 10\) and \(d_2=15\).
\(A=\frac{1}{2}\times10\times15\)
First, calculate \(10\times15 = 150\), then \(\frac{1}{2}\times150=75\).

Answer:

75