The Area of a Rhombus is Equal to Half the Product of its Diagonals

Here we will prove that the area of a rhombus is equal to half the product of its diagonals.

Solution:

Given:

PQRS is a rhombus whose diagonals are PR and QS. The diagonals intersect at O.

To prove: ar(rhombus PQRS) = $$\frac{1}{2}$$ ×PR × QS.

 Statement Reason 1. ar(∆RSQ) = $$\frac{1}{2}$$ ×Base × Altitude                  = $$\frac{1}{2}$$ ×QS × RO. 1. QS ⊥ PR, because diagonals of a rhombus are perpendicular to each other. 2. ar(∆PQS) = $$\frac{1}{2}$$ ×Base × Altitude                  = $$\frac{1}{2}$$ ×QS × PO. 2. As in reason 1. 3. ar(∆RSQ) + ar(∆PQS)                   = $$\frac{1}{2}$$ ×QS × (RO + PO). 3. By addition from statements 1 and 2. 4. ar(rhombus PQRS) = $$\frac{1}{2}$$ ×PR × QS. 4. By addition axiom for area.

9th Grade Math

From The Area of a Rhombus is Equal to Half the Product of its Diagonals to HOME PAGE

Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.

New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.

Share this page: What’s this?

Recent Articles

1. Constructing a Line Segment |Construction of Line Segment|Constructing

Aug 14, 24 09:52 AM

We will discuss here about constructing a line segment. We know how to draw a line segment of a certain length. Suppose we want to draw a line segment of 4.5 cm length.

Read More

2. Construction of Perpendicular Lines by Using a Protractor, Set-square

Aug 14, 24 02:39 AM

Construction of perpendicular lines by using a protractor is discussed here. To construct a perpendicular to a given line l at a given point A on it, we need to follow the given procedure

Read More

3. Construction of a Circle | Working Rules | Step-by-step Explanation |

Aug 13, 24 01:27 AM

Construction of a Circle when the length of its Radius is given. Working Rules | Step I: Open the compass such that its pointer be put on initial point (i.e. O) of ruler / scale and the pencil-end be…

Read More

4. Practical Geometry | Ruler | Set-Squares | Protractor |Compass|Divider

Aug 12, 24 03:20 PM

In practical geometry, we study geometrical constructions. The word 'construction' in geometry is used for drawing a correct and accurate figure from the given measurements. In this chapter, we shall…

Read More

5. Worksheet on Word Problems on Fractions | Fraction Word Problems | Ans

Aug 12, 24 02:23 AM

In worksheet on word problems on fractions we will solve different types of word problems on multiplication of fractions, word problems on division of fractions etc... 1. How many one-fifths

Read More