FIND THE MISSING DIMENSION OF TRAPEZOID

A trapezoid is also known as a trapezium is a four-sided polygon or a quadrilateral. It has one set of opposite sides which are parallel and a set of non-parallel sides.

The parallel sides are known as the bases and the non-parallel sides are known as the legs of the trapezoid.

Area of trapezoid = (1/2) h (a + b)

Here a and b area parallel sides and h is height.

Perimeter of the trapezoid = Sum of length of all sides.

Find x.

Problem 1 :

Solution :

So, the value of x is 6.

Problem 2 : 

Solution :

Area of trapezoid A = (1/2) h (a + b)

Area = 88 ft², a = 3 ft, b = 13 ft and h = x

88 = (1/2) ⋅ h (3 + 13)

Multiply by 2 on both sides

88 ⋅ 2 = x (16)

Divide by 16 on both sides.

(88 ⋅ 2)/16 = h

h = 11

Problem 3 :

Solution :

Area of trapezoid A = (1/2) h (a + b)

Area = 114 yd², a = 4 yd, b = x and h = 19 yd

114 = (1/2) ⋅ 19 (4 + x)

(114 ⋅ 2) = 19 (4 + x)

Divide by 19 on both sides.

(114 ⋅ 2)/19 = 4 + x

4 + x = 12

Subtracting 4 on both sides.

x = 8

So, base length of the trapezoid is 8 yd.

Problem 4 :

Solution :

Area of trapezoid A = (1/2) h (a + b)

Area = 56 yd², a = 14 yd, b = 2 yd and h = x

56 = (1/2) ⋅ x (14 + 2)

(56 ⋅ 2) = x (16)

Divide by 16 on both sides.

(56 ⋅ 2)/16 = x

x = 7 yd

So, height of the trapezoid is 7 yd.

Problem 5 :

Solution :

Area of trapezoid A = (1/2) h (a + b)

Area = 96 ft², a = 6 ft, b = x and h = 8 ft

96 = (1/2) ⋅ 8 (6 + x)

96 = 4 (6 + x)

Divide by 4 on both sides.

96/4 = 6 + x

6 + x = 24

Subtracting 6 on both sides.

x = 24 - 6

x = 18 ft

Problem 6 :

Solution :

Area of trapezoid A = (1/2) h (a + b)

Area = 75 ft², a = 7 ft, b = x and h = 5 ft

75 = (1/2) ⋅ 5 (7 + x)

Divide by 4 on both sides.

75/5 = (1/2) (7 + x)

(1/2) (7 + x) = 15

6 + x = 24

Subtracting 6 on both sides.

x = 24 - 6

x = 18 ft

Problem 7 :

Solution :

Area of trapezoid A = (1/2) h (a + b)

Area = 40 in², a = 9 in, b = 11 in and h = x in

40 = (1/2) ⋅ x (9 + 11)

Multiply by 2 on both sides.

(40⋅2) = x(20)

Divide by 20 on both sides.

x = 2⋅2

x = 4 in

Problem 8 :

Solution :

Area of trapezoid A = (1/2) h (a + b)

Area = 50 yd², a = 15 in, b = 10 yd and h = x yd

50 = (1/2) ⋅ x (15 + 10)

Multiply by 2 on both sides.

(50⋅2) = x(25)

Divide by 25 on both sides.

x = 100/25

x = 4 yd

Problem 9 :

Solution :

Area of trapezoid A = (1/2) h (a + b)

Area = 22 in², a = 9 in, b = x and h = 4 in

22 = (1/2) ⋅ 4 (9 + x)

Multiply by 2 on both sides.

(22⋅2) = 4(9+x)

Divide by 4 on both sides.

9 + x = 44/4

x = 11 - 9

x = 2 in

x = 4 yd