Question

verona is finding the area of a kite. she breaks up the figure into two triangles, as shown. does verona have enough information to determine the areas of both triangles? yes, each triangle has a base of 10 meters and a height of 3 meters. no, each triangle has a base of 10 meters, but the heights of the triangles cannot be determined. no, each triangle has a base of 6 meters, but there is not enough information to determine the heights of the triangles. yes, each triangle has a base of 6 meters. one triangle has a height of 2 meters and the other has a height of 8 meters.

Explanation:

Step1: Recall the formula for the area of a triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times base\times height\).

Step2: Analyze the given information

The total length of the two - part height of the kite is \(6m\). When the kite is split into two triangles, if we assume the base of each triangle is \(10m\) (the length of the diagonal which is the common side of the two triangles formed from the kite). The total height related to the base of \(10m\) is \(6m\). Since the two triangles share the base of \(10m\), and the sum of their heights (with respect to the base of \(10m\)) is \(6m\). If we consider each triangle, for a base \(b = 10m\), and let the heights of the two triangles be \(h_1\) and \(h_2\) such that \(h_1+h_2=6m\). We can assume \(h_1 = h_2=3m\) (because of the symmetry of the kite - like figure when split into two triangles along one of its diagonals).

Step3: Check each option

• Option 1:

If the base \(b = 10m\) and height \(h=3m\) for each triangle. Using the formula \(A=\frac{1}{2}\times b\times h\), for each triangle \(A=\frac{1}{2}\times10\times3 = 15m^{2}\). This option is correct as we can assume the height (due to the nature of the kite split into two triangles along a diagonal)

• Option 2:

The base of the triangles (when considering the formula for area with respect to the split) is \(10m\) (the diagonal of the kite), not \(6m\). And we can determine the height (as explained above)

• Option 3:

The base for calculating the area of the triangles (using the split shown) is \(10m\) (the diagonal of the kite), not \(6m\)

• Option 4:

The base of the triangles (using the split and formula for area of triangle) is \(10m\) (the diagonal of the kite), not \(6m\)

Answer:

Yes, each triangle has a base of 10 meters and a height of 3 meters.