HOW TO FIND THE AREA OF A TRIANGLE

Find the area of each triangle :

Problem 1 :

Solution :

By observing the figure,

Base (b) = 5 cm and Height (h) = 8 cm

Area of a triangle A = 1/2 (b × h)

= 1/2 (5 × 8)

Area = 20 cm²

Problem 2 :

Solution :

By observing the figure,

Base (b) = 10 in and Height (h) = 5 in

Area of a triangle A = 1/2 (b × h)

= 1/2 (10 × 5)

= 25 in².

Problem 3 :

Solution :

By observing the figure,

Base (b) = 25 yd and Height (h) = 4 yd

Area of a triangle A = 1/2 (b × h)

= 1/2 (25 × 4)

= 50 yd²

Problem 4 :

Solution :

By observing the figure,

Base (b) = 3.5 ft and Height (h) = 4 ft

Area of a triangle A = 1/2 (b × h)

= 1/2 (3.5 × 4)

= 7 ft²

Problem 5 :

The front part of a tent is 8 feet long and 5 feet tall. what is the area of the front part of the tent ?

Solution :

Given,

The front part of a tent = 8 feet long

The front part of a tent  = 5 feet tall

Area A = 1/2 (b × h)

Here base (b) = 8 feet and Height (h) = 5 feet

= 1/2 (8 × 5)

= 20 cm²

So, the area of the front part of the tent is 20 cm².

Problem 6 :

Kathy is playing a board game. The game pieces are each in the shape of a triangle. Each triangle has a base of 1.5 inches and a height of 2 inches. What is the area of a game piece? 

Solution :

Given, 

Base of a game piece (b) = 1.5 inches

Height of a game piece (h) = 2 inches

To find the area of a game piece,

Area of a triangle A = 1/2 (b × h)

= 1/2 (1.5 × 2)

Area = 1.5 in².

So, the area of a game piece = 1.5 in². 

Problem 7 :

A triangular – shaped window has a base of 3 feet and a height of 4 feet. What is the area of the window ?

Solution :

Given,

Base of the window (b) = 3 feet

Height of the window (h) = 4 feet

To find the area of the window,

Area of a triangle A = 1/2 (b × h)

= 1/2 (3 × 4)

Area = 6 ft²

So, the area of the window = 6 ft².

Problem 8 :

Landon has a triangular piece of paper. The base of the paper is 6  1/2 inches. The height of the paper is 8 inches. What is the area of the piece of paper ?

Solution :

Given,

Base of the paper (b) = 6  1/2 inches

Height of the paper (h) = 8 inches.

To find the area of the piece of paper,

Area of a triangle A = 1/2 (b × h)

= 1/2 ((6/2) × 8)

= 1/2  (3 × 8)

= 1/2 (24)

= 12 in²

So, the area of the piece of paper = 12 in².

Problem 9 :

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, height = 18 cm

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

= (1/2) x 36 x 18

= 18 x 18

= 324 square cm.

Problem 10 :

Estimate the area of the cottonwood leaf.

Solution :

Area of cotton wood = 1/2 x 4 x 5

= 2 x 5

= 10 square inches

Problem 11 :

The wingspan of the triangular hang glider is 30 feet.

a. How much fabric is needed to make the sail?

Solution :

Base = 30 ft and height = 9 ft

Area of triangle = (1/2) x 30 x 9

= 15 x 9

= 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 :

Area of sail A = (1/2) x 3 x 4

= 6 square meter

Area of sail B = (1/2) ⋅ 3x ⋅ 4x

= 6x² square meter

So, area of Sail B is x² square meter greater than area of Sail A.

Problem 13 :

If the area of a square with side a is equal to the area of a triangle with base a then the altitude of the triangle is :

a)  a/2      b)  a      c)  2a     d)  4a

Solution :

Area of square with side length a = a²

Area of square = area of triangle

a² = (1/2) x a x height

a² = (a/2) x height

height = 2a²/a

= 2a

So, the altitude of the triangle is 2a, option c is correct.

Problem 14 :

If the area of triangle is 1176 cm² and base corresponding altitude is 3 : 4, then the altitude of the triangle is :

a)  42 cm      b)  52 cm      c)  54 cm    d)  56 cm

Solution :

Area of the triangle = 1176 cm²

Base = 3x and height = 4x

(1/2) ⋅ 3x ⋅ 4x = 1176

6x² = 1176

x² = 1176/6

x² = 196

x = 14

Base = 3(14) ==> 42 cn

Height = 4(14) ==> 56 cm

So, the altitude is 56 cm, option d is correct.