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?
28 cm2
31.5 cm2
14.5 cm2
63 cm2
The correct answer is 63 cm2. To find the area of a rhombus, use this formula:
\(A=bh\)
The base (b) is 7 cm and the height (h) is 9 cm.
\(A=(9)(7)=63\text{ cm}^2\)
What is the area of this trapezoid?
147 ft2
228 ft2
375 ft2
456 ft2
The correct answer is 228 ft2. The formula for area of a trapezoid is:
\(A=\frac{1}{2}(b_1+b_2)h\)
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.
\(A=\frac{1}{2}(17+21)(12)=\frac{1}{2}(38)(12)=228\text{ ft}^2\)
What is the area of this rhombus?
88 in2
44 in2
38 in2
79 in2
The correct answer is 88 in2. The formula for area of a rhombus is:
\(A=bh\)
The base (b) is 11 in and the height (h) is 8 in.
\(A=(11)(8)=88\text{ in}^2\)
What is the area of this trapezoid?
39 cm2
30 cm2
25 cm2
36 cm2
The correct answer is 36 cm2. The formula for area of a trapezoid is:
\(A=\frac{1}{2}(b_1+b2)h\)
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.
\(A=\frac{1}{2}(7+11)(4)=\frac{1}{2}(18)(4)=36\text{ cm}^2\)
What is the area of this rhombus?
157 in2
259 in2
315 in2
427 in2
The correct answer is 315 in2. The formula for area of a rhombus is:
\(A=bh\)
Since a rhombus has 4 congruent sides, the length of the base (b) is 21 in. The height is 15 in.
\(A=(21)(15)=315\text{ in}^2\)