Answer:
- 128 m²
- 120 cm²
Explanation:
You want the areas of a kite and a rhombus, given certain segment lengths.
Area formula
The area of a quadrilateral in which the diagonals cross at right angles can be found from ...
A = (1/2)(d1·d2) . . . . . where d1 and d2 are the lengths of the diagonals.
1. Kite
The vertical diagonal is 6m +10m = 16m. The horizontal diagonal is 8m +8m = 16m.
The area is ...
A = (1/2)(16m)(16m) = 128 m²
The area of the kite is 128 square meters.
2. Rhombus
Each triangle is a right triangle, so the missing half-diagonal length is ...
d2 = √(13² -5²) = √144 = 12
The area is ...
A = (1/2)(2·5 cm)(2·12 cm) = 120 cm²
The area of the rhombus is 120 square centimeters.
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Additional comment
You can save the trouble of using the Pythagorean theorem to find the missing rhombus diagonal if you remember the Pythagorean triple {5, 12, 13}. That triple, along with {3, 4, 5}, {7, 24, 25}, {8, 15, 17}, and (9, 40, 41} are among those commonly seen in algebra, trig, and geometry problems.
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