FINDING THE AREA OF TRIANGLE WITH BASE AND HEIGHT

Problem 1 :

Solution :

Given, base = 6 km

Height = 6 km

Area of triangle = 1/2 × b × h

= 1/2 × 6 × 6

= 18 km²

So, the area of triangle is 18 km².

Problem 2 :

Solution :

Given, base = 9 cm

Height = 2 cm

Area of triangle = 1/2 × b × h

= 1/2 × 9 × 2

= 9 cm²

So, the area of triangle is 9 cm².

Problem 3 :

Solution :

Given, base = 12 cm

Height = 3 cm

Area of triangle = 1/2 × b × h

= 1/2 × 12 × 3

= 18 cm²

So, the area of triangle is 18 cm².

Problem 4 :

Solution :

Given, base = 15 m

Height = 12 m

Area of triangle = 1/2 × b × h

= 1/2 × 15 × 12

= 90 m²

So, the area of triangle is 90 m².

Problem 5 :

Solution :

Given, base = 10.7 km

Height = 3.4 km

Area of triangle = 1/2 × b × h

= 1/2 × 10.7 × 3.4

= 18.19 km²

So, the area of triangle is 18.19 km².

Problem 6 :

Solution :

Given, base = 24 ½ ft = 49/2 ft

Height = 8 ft

Area of triangle = 1/2 × b × h

= 1/2 × 49/2 × 8

= 98 ft²

So, the area of triangle is 98 ft².

Find the missing dimension.

Problem 7 :

Base: 4 in

Area: 22 in²

Solution:

Area of triangle = 1/2 × b × h

22 = 1/2 × 4 × h

22 = 2h

h = 11 in

So, the height of triangle is 11 in.

Problem 8 :

Height: 1 yd

Area = 2.5 yd²

Solution :

Area of triangle = 1/2 × b × h

2.5 = 1/2 × b × 1

2.5 = b/2

b = 5 yd

So, the base of triangle is 5 yd.

Problem 9 :

Base: 5 ft

Area: 5 5/6 ft² = 35/6 ft²

Solution :

Area of triangle = 1/2 × b × h

35/6 = 1/2 × 5 × h

35/6 = 5/2 × h

h = (35/6) × (2/5)

h = 7/3 ft

So, the height of triangle is 7/3 ft.

Problem 10 :

A shelf has the shape of a triangle. The base of the shelf is 36 centimeters, and the height is 18 centimeters. Find the area of the shelf.

Solution :

Base = 36 cm and height = 18 cm

Area of shelf = (1/2) x base x height

= (1/2) x 36 x 18

= 18 x 18

= 324 square cm

Problem 11 :

The wingspan of the triangular hang glider is 30 feet.

How much fabric is needed to make the sail?

Solution :

Area of fabric needed = (1/2) x base x height

Wingspan = 30 feet and height = 9 ft

= (1/2) x 9 x 30

= 9 x 15

= 135 square feet

Problem 12 :

The base and the height of Sail B are x times greater than the base and the height of Sail A. How many times greater is the area of Sail B? Write your answer as a power.

Solution :

Base of sail A = 3 m and height = 4 m

Area of sail A = (1/2) ⋅ 3 ⋅ 4

= 6

Base of sail B = 3x

Height of sail B = 4x

Area of sail B = (1/2) ⋅ 3x ⋅ 4x

= 6x²

Area of sail B is x² times area of sail A.

Problem 13 :

The total area of the polygon is 176 square feet. Find the value of x.

Solution :

Total area of polygon = 176 square feet

Area of rectangle + 2(area of triangle) = 176

length of rectangle = 16 ft and width = 8 ft

16(8) + 2(1/2) ⋅ x ⋅ 8 = 176

16(8) + 8x = 176

128 + 8x = 176

8x = 176 - 128

8x = 48

x = 48/8

x = 6

So, the value of x is 6 ft.

Problem 14 :

A wildlife conservation group buys a plot of land. How much land does it buy?

Solution :

Length of triangle = 6 miles and height = 3 miles

Area of triangle = (1/2) x 6 x 3

= 9 square feet

So, area of land is 9 square feet.

Problem 15 :

A sheet of plywood is 4 feet wide by 8 feet long. What is the minimum number of sheets of plywood needed to cover the frame? Justify your answer.

Solution :

Number of sheets = area of frame / area of sheet

= (1/2) x 24 x 8 / (4 x 8)

= (12 x 8) / (4 x 8)

= 96/32

= 3

So, the required number of sheets is 3.