Prove that the area of a rhombus is one-half the product of the lengths of the diagonals. Suppose that Delta ABCis equilateral triangle and that P is a point in the interior of this triangle. Prove that the sum of the perpendicular distances from P to each of the sides of the triangle is equal to the height of the triangle. Prove that the area of a triangle is equal to one-half the product of its perimeter and the length of the radius of a circle inscribed within the triangle. Prove that the diagonal of a kite connecting the vertices where the congruent sides intersect bisects the angles at these vertices and is the perpendicular bisector of the other diagonal. (Use the strict definition of a kite which is a quadrilateral with two distinct pairs of congruent adjacent sides.)
Mariyah Bell
Answered question
2022-10-14
2. Suppose that is equilateral triangle and that P is a point in the interior of this triangle. Prove that the sum of the perpendicular distances from P to each of the sides of the triangle is equal to the height of the triangle.
3. Prove that the area of a triangle is equal to one-half the product of its perimeter and the length of the radius of a circle inscribed within the triangle.
4. Prove that the diagonal of a kite connecting the vertices where the congruent sides intersect bisects the angles at these vertices and is the perpendicular bisector of the other diagonal. (Use the strict definition of a kite which is a quadrilateral with two distinct pairs of congruent adjacent sides.)
Answer & Explanation
t5an1izqp
Beginner2022-10-15Added 13 answers
Then
The area of rhombus ABCD divided diagonal in four parts
So area of rhombus ABCD =area of triangle AOD+area of triangle AOB+area of triangle BOC+area of triangle COD
=
=
=
=
So area of rhombus is equal to half of the product of diagonals....
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