What is the area of the figure below?
45 in², 90 in², 135 in², 180 in²

Solution:

The figure drawn above is a rhombus with diagonals 12 inches and 15inches respectively.

The property of the rhombus which is reflected here is that the diagonals bisect each other at right angles.

Hence the area of the rhombus can be expressed as the sum of all the four triangles formed by the diagonals:

All the four triangles are right-angled triangles with sides 6 inches (12/2) and 7.5 inches(15/2) respectively.

The area of each triangle is:

Area of triangle = (1/2)(base)(height)

= (1/2)(6)(7.5)

= (1/2)(6)(15/2)

= 45/2

= 22.5 inches²

Since there are four triangles of the same area, the area of the rhombus is:

Area of Rhombus = 4 × 22.5 = 90 in²

Aliter:

Given: The measures as half of the diagonals = 6 inches and 7.5 inches respectively.

The property of the rhombus which is reflected here is that the diagonals bisect each other at right angles.

Thus diagonal 1 = 2 × 6 = 12 inches and 

diagonal 2 = 2 × 7.5 = 15 inches

Area of the rhombus = 1/2 × diagonal 1 × diagonal 2

= 1/2 ×12 ×15

= 6 × 15 

= 90 in² 

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What is the area of the figure below?
45 in², 90 in², 135 in², 180 in²

Summary:

The area of the figure which is a rhombus is 90 inches².