How to Find the Area of a Trapezoid and Rhombus
Hi, and welcome this video lesson on special types of quadrilaterals. Today we’re going be talking about trapezoids and rhombuses. Now if you’re looking for something on a normal quadrilateral, go ahead check our video out entitled common quadrilaterals.
For now, let’s get started on defining some of these objects. A trapezoid is a quadrilateral where at least 1 pair of sides are parallel. The parallel sides are called the bases, and the other 2 remaining sides are called legs.
Finding the area of one of these can be a bit trickier than other objects. The most common used equation is the following: Area is equal to the 2 bases, divided by 2, times H, or the height.
A rhombus is a little bit different. It’s a parallelogram where all 4 sides are of equal length and opposite angles are equal. Most often, it is referred to as a diamond.
To find the area of a rhombus, you can multiply the imaginary perpendicular lines that travel in the middle of a rhombus and divide the result by 2. Like this: L times M, divided by 2 is equal to the area. I hope that helps. Thanks for watching this video lesson and until next time, happy studying.
Area of a Trapezoid and Rhombus Practice Questions
What is the area of this rhombus?
The correct answer is 63 cm2. To find the area of a rhombus, use this formula:
[latex]A=bh[/latex]
The base (b) is 7 cm and the height (h) is 9 cm.
[latex]A=(9)(7)=63\text{ cm}^2[/latex]
What is the area of this trapezoid?
The correct answer is 228 ft2. The formula for area of a trapezoid is:
[latex]A=\frac{1}{2}(b_1+b_2)h[/latex]
The length of base 1 (b1) is 17 ft. The length of base 2 (b2) is 21 feet. And the height (h) is 12 ft.
[latex]A=\frac{1}{2}(17+21)(12)=\frac{1}{2}(38)(12)=228\text{ ft}^2[/latex]
What is the area of this rhombus?
The correct answer is 88 in2. The formula for area of a rhombus is:
[latex]A=bh[/latex]
The base (b) is 11 in and the height (h) is 8 in.
[latex]A=(11)(8)=88\text{ in}^2[/latex]
What is the area of this trapezoid?
The correct answer is 36 cm2. The formula for area of a trapezoid is:
[latex]A=\frac{1}{2}(b_1+b2)h[/latex]
The length of base 1 (b1) is 7 cm. The length of base 2 (b2) is 11 cm. The length of the height (h) is 4 cm.
[latex]A=\frac{1}{2}(7+11)(4)=\frac{1}{2}(18)(4)=36\text{ cm}^2[/latex]
What is the area of this rhombus?
The correct answer is 315 in2. The formula for area of a rhombus is:
[latex]A=bh[/latex]
Since a rhombus has 4 congruent sides, the length of the base (b) is 21 in. The height is 15 in.
[latex]A=(21)(15)=315\text{ in}^2[/latex]