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A kite has a diagonal of 3 inches and area of 12 in2. What is the length of the remaining diagonal?
This time, instead of solving for area, we can use the area formula for a kite to solve for the missing diagonal. Whether we solve for d1 or d2 doesn't really matter since we'll have to plug 3 inches in for the other anyway.
12 = 1.5d2 d2 = 8 inches
The kite has diagonals of 3 inches and 8 inches.
What is the area of the following kite?
To find the area, we need the length of both diagonals. For now, we know that one of the diagonals is 17 feet long, but the other diagonal is unknown. If we look at the individual triangles the make up the kite, we can see that we have a leg (10 ft) and a hypotenuse (13 ft). That's enough to solve for the remaining leg.
a2 + b2 = c2 102 + b2 = 132 100 + b2 = 169
The leg we've found is only half of the missing diagonal. The diagonal is ft, or about 16.6 ft. Now that we have the lengths of both diagonals, we can find the area.
A ≈ 141.1 ft2
A kite has a side length of 7 m and a perimeter of 20 m. If the shorter diagonal has a length of 4 m, what is the area of the kite?
We know that kites have two pairs of congruent sides. If one side is 7 m long, then we have another side of the same length. The remaining 6 m of perimeter is split up evenly too, so we have two sides of length 7 m and two sides of length 3 m.
We know that the shorter diagonal is 4 m long, which means we can find the length of the other diagonal using the Pythagorean Theorem for each portion of the unknown diagonal. The first triangle has a leg of 2 m and a hypotenuse of 3 m.
a2 + b2 = c2 22 + b2 = 32 b2 = 5
The other triangle has a leg of 2 m and a hypotenuse of 7 m.
a2 + b2 = c2 22 + b2 = 72 b2 = 45
If we combine them, we can see that the unknown diagonal has a length of . Calculating the area shouldn't be a problem now.