A rhombus has a 68 cm perimeter and a 16 cm diagonal. Find its area.
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Answer: B. 240 cm2
Explanation
Dividing the rhombus perimeter of sixty eight centimeters by four gives a side length of seventeen centimeters. Applying the Pythagorean theorem to the half diagonals yields the other diagonal length of thirty centimeters. Multiplying one half by the product of both diagonals gives an area of two forty square centimeters. All four sides of a rhombus are equal in length by definition. The diagonals of a rhombus bisect each other at right angles forming four congruent triangles. The area of a rhombus can be calculated using the lengths of its two perpendicular diagonals.
Architects and tile designers calculate rhombus surface areas for geometric flooring and mosaic patterns. Structural engineers analyze diamond shaped bracing frameworks using diagonal length relationships. Fabricators cut rhombus shaped metal panels ensuring structural symmetry and precise dimensions. Option a overestimates the area due to incorrect calculation of the secondary diagonal. Option c assumes a larger diagonal length than permitted by the side measurement. Option d results from using an incorrect multiplier in the diagonal area formula.
- Subject
- Mathematics
- Category
- Mathematics
- Topic
- —
- Difficulty
- medium
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