Question Video: Finding the Area of a Rhombus Inscribed in a Rectangle | Nagwa Question Video: Finding the Area of a Rhombus Inscribed in a Rectangle | Nagwa

Question Video: Finding the Area of a Rhombus Inscribed in a Rectangle Mathematics • Second Year of Preparatory School

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The figure shows a rhombus within a rectangle. Find the area of the rhombus to two decimal places.

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Video Transcript

The figure shows a rhombus within a rectangle. Find the area of the rhombus to two decimal places.

Looking at the diagram, we notice that the vertices of the rhombus are each at the midpoint of one of the rectangle sides. We know this because these line markers indicate that, for example, line segment π΄π is the same length as line segment ππ·. From this, we can deduce that the diagonals of the rhombus, thatβs ππ and ππ, are each parallel to one side of the rectangle. And so it follows that theyβre also the same length as the rectangle sides. So ππ is 15.8 centimeters and ππ is 30.3 centimeters.

We can then recall that the area of a rhombus is equal to half the product of the lengths of its diagonals. If the lengths of the diagonals are π one and π two, then the area of a rhombus is π one multiplied by π two over two. So the area of the rhombus ππππ is equal to the length of ππ multiplied by the length of ππ over two. Thatβs 30.3 multiplied by 15.8 over two, which is 293.37 square centimeters.

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