Area and Perimeter Word Problems

**Page 3**

21.

What is the height of the triangle, if the base of the triangle is twice the height, and its area is 225 ft^{2}?

a. | 16 ft | ||

b. | 19 ft | ||

c. | 15 ft | ||

d. | None of the above |

Given, area of the triangle = 225 ft

The base = twice the height = 2 ×

Area of a triangle =

[Formula.]

225 =

[Substitute the values.]

225 =

[Simplify.]

[Taking square root on both sides.]

15 =

The height of the triangle = 15 ft.

Correct answer : (3)

22.

What is the height of the triangle, if the triangle and the parallelogram have the same base and the same area?

a. | $h$ = 2H | ||

b. | H = $h$ | ||

c. | 2$h$ = H | ||

d. | None of the above |

Height of the parallelogram = H

Height of the triangle =

Area of the triangle =

Area of the parallelogram = base × height

Given, area of the triangle = area of the parallelogram

[Substitute the area formulae.]

[Bases are equal.]

[Substitute the height values.]

Correct answer : (1)

23.

The area of a parallelogram is half of the area of the triangle. What is the height of the triangle, if they have the same base length of 6 cm and the area of the parallelogram is 39 cm^{2}?

a. | 26 cm | ||

b. | 21 cm | ||

c. | 31 cm | ||

d. | None of the above |

The area of the parallelogram =

[Given.]

39 =

[Substitute the area of parallelogram.]

78 = area of the triangle

[Multiply each side by 2.]

Area of the triangle = 78 cm

Base length of the parallelogram = base length of the triangle = 6cm

[Given.]

Area of the triangle =

[Formula.]

78 =

[Substitute the values.]

78 = 3 x height

[Multiply 3 with

[Divide each side by 3.]

Height of the triangle = 26 cm

[Simplify.]

Correct answer : (1)

24.

What is the base length of the parallelogram, if the height is half of the base and its area is 128 in.^{2}?

a. | 21 in | ||

b. | 18 in | ||

c. | 16 in | ||

d. | None of the above |

Height of the parallelogram = half of the base =

Area of the parallelogram = base × height

[Formula.]

128 =

[Substitute the values.]

128 × 2 =

[Multiply each side by 2.]

256 =

[Simplify.]

[Taking square root on both sides.]

16 =

The base length of the parallelogram = 16 in.

Correct answer : (3)

25.

What is the area of ADB in the figure?

a. | 48 in. ^{2} | ||

b. | 12 in. ^{2} | ||

c. | 24 in. ^{2} | ||

d. | None of the above |

Base of the triangle ADB = 6 in. and the height of the triangle ADB = 4 in.

Area of the triangle ADB =

[Formula.]

[Substitute the values.]

= 12

[Simplify.]

The area of ADB = 12 in.

Correct answer : (2)

26.

Split the trapezoid into a triangle and a parallelogram and find the area of the trapezoid.

a. | 20 m. ^{2} | ||

b. | 30 m. ^{2} | ||

c. | 25 m. ^{2} | ||

d. | 15 m. ^{2} |

Let the line touch AB on the point E.

Now the trapezoid is split into a parallelogram DEBC and a Δ ADE.

Base length of the parallelogram = BE = DC = 6 m., height = 4 m.

Area of a parallelogram DEBC = base × height = 6 × 4 = 24 m.

Base length of the Δ ADE = AE = AB - DC = 9 - 6 = 3 m.

Height of the Δ ADE = 4 m.

Area of the Δ ADE =

Area of the trapezoid ABCD = Area of a parallelogram DEBC + Area of the Δ ADE.

Area of the trapezoid ABCD = 24 + 6 = 30 m.

Correct answer : (2)

27.

Find the perimeter of the figure.

a. | 24 in. | ||

b. | 48 in. | ||

c. | 12 in. | ||

d. | 10 in. |

From the figure AB = 8 in., BC = 10 in., AC = 6 in.

Perimeter of ΔABC = AB + BC + CA

= 8 + 10 + 6

[Substitute the values.]

= 24

So, the perimeter of the figure is 24 in.

Correct answer : (1)

28.

Find the perimeter of ΔABC in the figure.

a. | 12 in. | ||

b. | 18 in. | ||

c. | 21 in. | ||

d. | 3 in. |

From the figure, AB = 3 in., BC = 10 in. and AC = 8 in.

Perimeter of ΔABC = AB + BC + CA

= 3 + 10 + 8

[Substitute the values.]

= 21

[Add.]

The perimeter of the ΔABC is 21 in.

Correct answer : (3)

29.

Find the perimeter of the parallelogram shown.

a. | 10 in. | ||

b. | 20 in. | ||

c. | 5 in. | ||

d. | 16 in. |

From the figure, AB = 5 in. and AD = 3 in.

As the lengths of the parallel sides are equal, AB = CD = 5 in., AD = BC = 3 in.

Perimeter of the parallelogram = AB + BC + CD + DA

= 5 + 3 + 5 + 3

[Substitute the lengths.]

= 16

[Add.]

So, the perimeter of the parallelogram given in the figure is 16 in.

Correct answer : (4)

30.

Find the length of NO in the given triangle, if the perimeter is 35 ft.

a. | 7 ft | ||

b. | 11 ft | ||

c. | 6 ft | ||

d. | 8 ft |

Perimeter of a triangle = sum of all sides

[Formula.]

Perimeter of the triangle MNO = MN + NO + OM

[Formula.]

35 = 15 + NO + 13

[Substitute the values.]

35 = 28 + NO

[Add 15 and 13.]

35 - 28 = 28 -28 + NO

[Subtract 28 from each side.]

7 = NO

[Simplify.]

The length of NO of the triangle is 7 ft.

Correct answer : (1)