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

Step: 2

Area of the figure = area of square ABCD + area of rectangle DEFG + area of triangle CGH

Step: 3

= AB × AB + DE × EF + 1 2 × CG × GH

Step: 4

= 3 × 3 + 3 × 12 + 1 2 × 9 × 3

Step: 5

= 9 + 36 + 13.5

Step: 6

= 58.5 in^{2}

Correct Answer is : 72 in^{2}

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 × height × (sum of the measures of the parallel sides)

Step: 3

= 1 2 × height × (AD + BC)

Step: 4

= 1 2 × 4 × (16 + 12)

[Substitute AD = 16 in., BC = 12 in. and height = 4 in..]

Step: 5

= 1 2 × 4 × 28 = 56 in.^{2}

[Simplify.]

Step: 6

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

Step: 7

= 1 2 × 6 × 8

[Substitute FD = 6 in. and EF = 8 in..]

Step: 8

= 48 2 = 24 in.^{2}

[Simplify.]

Step: 9

So, area of the figure = 24 + 56 = 80 in.^{2}

[Substitute the values.]

Correct Answer is : 80 in.^{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

Step: 2

From the figure, AB = 4 m., BC = 6.5 m., CD = 3 m., DE = 3.5 m., EF = 9 m., FG = 3.5 m, GH = 2 m, HA = 6.5 m.

[GH = FE - (CD + AB).]

Step: 3

Perimeter of the figure = Sum of all the sides of the figure.

[Formula.]

Step: 4

Perimeter of the figure = AB + BC + CD + DE + EF + FG + GH + HA

Step: 5

4 + 6.5 + 3 + 3.5 + 9 + 3.5 + 2 + 6.5 = 38

[Substitute the values and add.]

Step: 6

Perimeter of the figure = 38 m.

Correct Answer is : 38 m

Step: 1

Step: 2

From the figure, AB = 17 m, BC = 15 m, CD = 17 m, DE = 3 m, EF = 8 m, FG = 9 m, GH = 8 m, HA = 3 m

Step: 3

Perimeter of the figure = Sum of all the sides of the figure.

[Formula.]

Step: 4

Perimeter of the figure = AB + BC + CD + DE + EF + FG + GH + HA

Step: 5

17 + 15 + 17 + 3 + 8 + 9 + 8 + 3 = 80 m

[Substitute the values and add.]

Step: 6

Perimeter of the figure = 80 m.

Correct Answer is : 80 cm

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

From the figure, diameter of the circle = side of the square = 15 cm.

Step: 2

Area of the circle = π (d 2 )^{2}

[Radius = diameter 2 ]

Step: 3

= 3.14 x (15 2 )^{2}

[Substitute the values.]

Step: 4

= 3.14 x (7.5)^{2}

[Divide 15 by 2.]

Step: 5

= 3.14 x 7.5 x 7.5

Step: 6

= 176.63

[Multiply.]

Step: 7

Area of the circle = 176.63 = 176.6 cm^{2}

Step: 8

Area of the square = side x side

[Formula.]

Step: 9

= 15 x 15

[Substitute the values.]

Step: 10

= 225

[Multiply.]

Step: 11

Area of the square = 225 cm^{2}

Step: 12

Area of the shaded region = Area of the square - Area of the circle

Step: 13

= 225 - 176.6

[Substitute the values.]

Step: 14

= 48.4

[Subtract.]

Step: 15

The area of the shaded region in the figure is 48.4 cm^{2}.

Correct Answer is : 48.4 cm^{2}

Step: 1

The total area of the figure = Area of the trapezoid ABEF + Area of the rectangle BCDE

Step: 2

Area of the trapezoid ABEF = (1 2 ) × height × (sum of the measures of the parallel sides)

Step: 3

= (1 2 ) × FO × (AF + BE)

Step: 4

= (1 2 ) × 1 × (4 +6)

[From the figure, FO = 1 ft, AF = 4 ft and BE = 6 ft.]

Step: 5

= (1 2 ) × 1 × 10

[Add 4 and 6 in the grouping symbol.]

Step: 6

= 5 ft^{2}

[Simplify.]

Step: 7

Area of the rectangle BCDE = length × width = BC × CD

Step: 8

= 1 × 6

[From the figure, BC = ED = 1 ft and BE = CD = 6 ft.]

Step: 9

= 6 ft^{2}

Step: 10

The total area of the figure = 5 + 6 = 11 ft^{2}

[Substitute the values.]

Correct Answer is : 11 ft^{2}

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}

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