Step: 1

The area of the figure = Area of the trapezoid ABCD + Area of the Δ DEF.

Step: 2

The area of the trapezoid ABCD = 1 2 x height x (sum of the measures of the parallel sides)

Step: 3

= 1 2 x height x (AD + BC)

Step: 4

= 1 2 x 2 x (10 + 6)

[Substitute AD = 10 m, BC = 6 m and height = 2 m.]

Step: 5

= 1 2 x 2 x 16 = 16 m^{2}

[Simplify.]

Step: 6

= 16 m^{2}

[Simplify.]

Step: 7

The area of ΔDEF= 1 2 x base x height = 1 2 x FD x EF

Step: 8

= 1 2 x 3 x 4

[Substitute FD = 3 m and EF = 4 m.]

Step: 9

= 12 2 = 6 m^{2}

[Simplify.]

Step: 10

So, area of the figure = 16 + 6 = 22 m^{2}

[Substitute the values.]

Correct Answer is : 22 m^{2}

Step: 1

The total area of the figure = area of the triangle ABC + area of the trapezoid CDEF.

Step: 2

The area of the triangle ABC = 1 2 × base × height

Step: 3

= (1 2 ) × BC × AO

Step: 4

= (1 2 ) × 3 × 2

[Substitute BC = 3 m and AO = 2 m.]

Step: 5

= 3 m ^{2}

[Simplify.]

Step: 6

The area of the trapezoid CDEF = (1 2 ) × height × (sum of the measures of the parallel sides)

Step: 7

= (1 2 ) × CS × (CF + DE)

Step: 8

= (1 2 ) × 2 × (4 + 6)

[Substitute CS = 2, CF = 4 and DE = 6.]

Step: 9

= (1 2 ) × 2 × 10

[Work inside the grouping symbols.]

Step: 10

= 10 m^{2}

[Simplify.]

Step: 11

The total area of the figure = 3 + 10 = 13 m^{2}.

[Substitute the values.]

Correct Answer is : 13 m^{2}

Step: 1

In the given figure, the area of ABCE is 40 cm^{2} and the area of ECD is 20 cm^{2}.

[Given.]

Step: 2

The area of ABCDE = area of ABCE - area of ECD

[From the given figure.]

Step: 3

= 40 - 20

[From step 1.]

Step: 4

= 20

[Subtract.]

Step: 5

Therefore, the area of the given figure ABCDE is 20 cm^{2} .

Correct Answer is : 20 cm^{2}

Step: 1

Diagonal AC divides the rectangle into two congruent triangles.

Step: 2

Area of the triangle ABC = 12 cm^{2}.

Step: 3

Area of the rectangle ABCD = 2 × area of traingle ABC.

= 2 × 12

Step: 4

So, the area of the rectangle ABCD = 24 cm^{2}.

Correct Answer is : 24 cm.^{2}

Step: 1

In the given figure, 52 squares are colored.

Step: 2

Area of each square = 1 square unit.

Step: 3

Area of 52 squares = 52 × 1 = 52 square units.

Correct Answer is : 52 square units

Step: 1

Step: 2

From the figure, Area of the rectangle ABFG = length × width = AG × AB = 7 × 4 = 28 sq.yd

Step: 3

Area of the rectangle CDEF = length × width = CD × DE = 5 × 2 = 10 sq.yd

Step: 4

Total area of the figure ABCDEFG = area of the rectangle ABFG + area of the rectangle CDEF

Step: 5

= 28 + 10 = 38

Step: 6

So, total area = 38 sq.yd

Correct Answer is : 38 yd^{2}

Step: 1

Label the given figure as shown below and draw line EH perpendicular to DF.

Step: 2

Area of rectangle ABCH = 8 × 4 = 32 sq ft.

[Area of rectangle = length × width.]

Step: 3

Area of triangle CDE = 1 2 × 10 × 4 = 20 sq ft.

[Area of triangle = 1 2 × base × height.]

Step: 4

Area of rectangle EFGH = 14 × 4 = 56 sq ft.

[Area of rectangle = length × width.]

Step: 5

The total area of the given figure ABCDEFGH = Area of rectangle ABCH + Area of triangle CDE + Area of rectangle EFGH.

Step: 6

= 32 + 20 + 56

[From steps 2, 3, and 4.]

Step: 7

= 108

[Add.]

Step: 8

Therefore, the total area of the given figure is 108 sq ft.

Correct Answer is : 108 sq ft

Step: 1

[Draw BF ¯ ⊥ ED ¯ .]

Step: 2

ABFE is a rectangle in which AB = EF = 6 cm and AE = BF = 7 cm. BCDF is a trapezium in which CD = 12 cm, BF = 7 cm and DF = 4 cm as shown.

Step: 3

Area of rectangle ABFE = 7 × 6 = 42 cm^{2}

[Area of a rectangle = length × width.]

Step: 4

Area of trapezoid = ( 1 2 )(4)(7 + 12) = 38 cm^{2}

[Area of trapezoid = 1 2 h (b _{1} + b _{2}).]

Step: 5

Total area of the figure = 42 + 38 = 80 cm^{2}

Correct Answer is : 80 cm^{2}

Step: 1

Step: 2

The given figure is divided into 3 rectangles.

Step: 3

Area of rectangle = length × width.

Step: 4

Area of rectangle ABFK = 7 × 6 = 42 sq in.

Step: 5

Area of rectangle BCDE = 4 × 3 = 12 sq in.

Step: 6

Area of rectangle GHIJ = 21 × 13 = 273 sq in.

Step: 7

Total area of the given figure ABCDEHGHIJK = Area of rectangle ABFK + Area of rectangle BCDE + Area of rectangle GHIJ.

Step: 8

= 42 + 12 + 273

[From steps 4, 5, and 6.]

Step: 9

= 327

[Add.]

Step: 10

Therefore, the total area of the given figure is 327 sq in.

Correct Answer is : 327 sq in.

Step: 1

Area of the figure = Area of A + Area of B + Area of C + Area of D

Step: 2

Area of A = Area of D

[The dimensions of A and D are the same.]

Step: 3

Area of A = Area of D = 1 cm × 10 cm = 10 cm^{2}

[Area of a rectangle = length × width.]

Step: 4

Area of B = Area of C

[The dimensions of B and C are the same.]

Step: 5

Area of B = Area of C = 1 2 × 6 cm × 8 cm = 24 cm^{2}

[Area of a triangle = 1 2 × base × height.]

Step: 6

Area of the figure = 10 cm^{2} + 24 cm^{2} + 24 cm^{2} + 10 cm^{2}

[Substitute the values.]

Step: 7

= 68 cm^{2}

[Add.]

Step: 8

Therefore, area of the figure is 68 cm^{2}.

Correct Answer is : 68 cm^{2}

Step: 1

The area of a composite 2-D shape can be found by finding the areas of individual shape and adding them up.

Step: 2

Area = Length × Width

Step: 3

Area A = 17 × 3 = 51 cm^{2}

Step: 4

Area B = 14 × 8 = 112 cm^{2}

Step: 5

Total area = 51 cm^{2} + 112 cm^{2} = 163 cm^{2}

Step: 6

So, the area of the given composite shape is 163 cm^{2}.

Correct Answer is : 163 cm^{2}

Step: 1

The area of a composite 2-D shape can be found by finding the areas of individual shape and adding them up.

Step: 2

Area = Length × Width

Step: 3

Area A = 7 × 7 = 49 cm^{2}

Step: 4

Area B = 4 × 4 = 16 cm^{2}

Step: 5

Total area = 49 cm^{2} + 16 cm^{2} = 65 cm^{2}

Step: 6

So, the area of the given composite shape is 65 cm^{2}.

Correct Answer is : 65 cm^{2}

Step: 1

The figure is divided into three rectangles.

Step: 2

Step: 3

Area of the figure = Area of rectangle ABCJ + Area of rectangle DEIJ + Area of rectangle FGHI

Step: 4

= AB × BC + JD × DE + IF × FG

Step: 5

= 12 × 3 + 5 × 6 + 15 × 3

Step: 6

= 36 + 30 + 45 = 111

Step: 7

Therefore, area of the figure is 111 m^{2}.

Correct Answer is : 111 m^{2}

Step: 1

Area of the figure = Area of trapezium FADE + Area of rectangle ABCD

Step: 2

= 1 2 × FG × (FE + AD) + AD × CD

Step: 3

= 1 2 × 3 × (3 + 7) + 7 × 5

Step: 4

= 15 + 35 = 50

Step: 5

Therefore, area of the figure is 50 m^{2}.

Correct Answer is : 50 m^{2}

Step: 1

The figure is divided into a square and a rectangle.

Step: 2

Area of the figure = Area of square CDEF + Area of rectangle ABGH

Step: 3

= DE × EF + AH × GH

[Area of rectangle = length × width, and Area of square = side × side.]

Step: 4

= 2 × 2 + 8 × 1 = 4 + 8 = 12

Step: 5

Therefore, area of the figure is 12 m^{2}.

Correct Answer is : 12 m^{2}

- Areas of Triangles-Gr 6-Solved Examples
- Net Figures made up of Rectangles and Triangles-Gr 6-Solved Examples

- Division