# AREAS OF TRIANGLES AND QUADRILATERALS WORKSHEET

Problem 1 :

Find the area of the figure ABCD shown below. Problem 2 :

Find the height of a triangle that has an area of 12 square units and base length is 6 units.

Problem 3 :

A triangle has an area of 52 square feet and a base of 13 feet. Are all triangles with these dimensions congruent.

Problem 4 :

Find the area of trapezoid WXYZ shown below. Problem 5 :

Find the area of the rhombus ABCD shown below. Problem 6 :

Find the area of roof of the house shown below.   Method 1 :

Use AB as the base. Then, b = 16 and h = 9.

Area of the figure ABCD is

= b ⋅ h

= 16 ⋅ 9

= 144 square units

Method 2 :

Use AD as the base. Then, b = 12 and h = 12.

Area of the figure ABCD is

= b ⋅ h

= 12 ⋅ 12

= 144 square units

Notice that we get the same area with either base.

Because we want to find height of the triangle, we have to rewrite the area formula such that h is alone on one side of the equation.

Formula to find area of a triangle :

A = 1/2 ⋅ ⋅ h

Multiply both sides by 2.

2A = ⋅ h

Divide both sides by b.

2A/b = h

Given : A = 12 and b = 6.

Then, we have

(2 ⋅ 12)/6 = h

4 = h

So, the height of the triangle is 4 units.

Because we want to find height of the triangle, we have to rewrite the area formula such that h is alone on one side of the equation.

Using formula from Problem 2, the height of the triangle is

h = (⋅ 52)/13

h = 8 feet

There area many triangles with these dimensions. Some are shown below.  The height of the trapezoid WXYZ above is

h = 5 - 1

h = 4 units

Find the lengths of the bases :

 b1 = YZb1 = 5 - 2b1 = 3 units b2 = XWb2 = 8 - 1b2 = 7

Formula to find area of a trapezoid :

A = 1/2 ⋅ h ⋅ (b1 + b2)

Substitute h = 4, b1 = 3 and b2 = 7.

A = 1/2 ⋅ 4 ⋅ (3 + 7)

A = 20

So, the area of trapezoid WXYZ is 20 square units. Let d1 and d2 represent lengths of the diagonals AC and BD respectively.

d= AC = 20 + 20 = 40 units

d= BD = 15 + 15 = 30 units

Formula to find area of a rhombus :

A = 1/2 ⋅ d1  d2

Substitute d1 = 40 and d2 = 30.

A = 1/2 ⋅ 30  40

A = 600

So, the area of rhombus ABCD is 600 square units. G, H and K are trapezoids and J is a triangle. The hidden back and left sides of the roof are the same as the front and right sides.

Area of J = 1/2 ⋅ 20 ⋅ 9 = 90 ft2

Area of G = 1/2 ⋅ 15 ⋅ (20 + 30) = 375 ft2

Area of H = 1/2 ⋅ 15 ⋅ (42 + 50) = 690 ft2

Area of K = 1/2 ⋅ 12 ⋅ (30 + 42) = 432 ft2

The roof has two congruent faces of each type.

So, the total area is

= 2(90 + 375 + 690 + 432)

= 2(1587)

= 3174

So, the total area of the roof is 3174 square feet.

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