# 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.

## Practice Questions

**Question #1:**

What is the area of this rhombus?

28 cm^{2}

31.5 cm^{2}

14.5 cm^{2}

63 cm^{2}

**Answer:**

The correct answer is 63 cm^{2}. 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.

\(A=(9)(7)=63\text{ cm}^2\)

**Question #2:**

What is the area of this trapezoid?

147 ft^{2}

228 ft^{2}

375 ft^{2}

456 ft^{2}

**Answer:**

The correct answer is 228 ft^{2}. The formula for area of a trapezoid is:

\(A=\frac{1}{2}(b_1+b_2)h\)

The length of base 1 (*b _{1}*) is 17 ft. The length of base 2 (

*b*) is 21 feet. And the height (

_{2}*h*) is 12 ft.

\(A=\frac{1}{2}(17+21)(12)=\frac{1}{2}(38)(12)=228\text{ ft}^2\)

**Question #3:**

What is the area of this rhombus?

88 in^{2}

44 in^{2}

38 in^{2}

79 in^{2}

**Answer:**

The correct answer is 88 in^{2}. The formula for area of a rhombus is:

\(A=bh\)

The base (*b*) is 11 in and the height (*h*) is 8 in.

\(A=(11)(8)=88\text{ in}^2\)

**Question #4:**

What is the area of this trapezoid?

39 cm^{2}

30 cm^{2}

25 cm^{2}

36 cm^{2}

**Answer:**

The correct answer is 36 cm^{2}. The formula for area of a trapezoid is:

\(A=\frac{1}{2}(b_1+b2)h\)

The length of base 1 (*b _{1}*) is 7 cm. The length of base 2 (

*b*) is 11 cm. The length of the height (

_{2}*h*) is 4 cm.

\(A=\frac{1}{2}(7+11)(4)=\frac{1}{2}(18)(4)=36\text{ cm}^2\)

**Question #5:**

What is the area of this rhombus?

157 in^{2}

259 in^{2}

315 in^{2}

427 in^{2}

**Answer:**

The correct answer is 315 in^{2}. 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.

\(A=(21)(15)=315\text{ in}^2\)