# PROBLEM SOLVING USING AREA OF TRIANGLES

Problem solving using area of triangles :

Here we are going to see some practical problems based on the concept area of triangle.

## Problem solving using area of triangles - Examples

Example 1 :

Each triangular face of the Pyramid of Peace in Kazakhstan is made up of 25 smaller equilateral triangles. These triangles have measurements as shown in the diagram. What is the area of one of the smaller equilateral triangles?

Solution :

Base of the triangle = 12 m

Height of the triangle = 10.4 m

Area of the triangle = (1/2) x b x h

=  (1/2) x 12 x 10.4

=  6 x 10.4 = 62.4 square meter

Example 2 :

Amy needs to order a shade for a triangular-shaped window that has a base of 6 feet and a height of 4 feet. What is the area of the shade?

Solution :

Since the shade is in the shape of triangle, we have to use the formula  for area of triangle to find the area of the shade.

Area of the triangle = (1/2) x b x h

base = 6 feet and height = 4 feet

=  (1/2) x 6 x 4 = 12 square feet

Hence the area of the shade is 12 square feet.

Example 3 :

Monica has a triangular piece of fabric. The height of the triangle is 15 inches and the triangle’s base is 6 inches. Monica says that the area of the fabric is 90 square inches . What error did Monica make? Explain your answer.

Solution :

To find the area of the fabric, we need to use the formula for the area of the triangle.

Area of triangle = (1/2) x b x h

height = 15 inches and base = 6 inches

=  (1/2) x 15 x 6

=  15 x 3 = 45 square inches

Actual area of the triangular piece of fabric is 45 square inches. But Monica says that area of the fabric is 90 square inches. Which means, she forgot to multiply the product of base and height by 1/2. This is the error that she made.

Example 4 :

The sixth-grade art students are making a mosaic using tiles in the shape of right triangles. The two sides that meet to form a right angle are 3 centimeters and 5 centimeters long. If there are 200 tiles in the mosaic, what is the area of the mosaic?

Solution :

base = 5 cm and height = 3 cm

Area of one tile = (1/2) x b x h

=  (1/2) x 5 x 3

=  7.5 cm²

Area of 200 tiles in the mosaic = 200 x 7.5

=  1500 cm²

Example 5 :

Wayne is going to paint the side of the house shown in the diagram. What is the area that will be painted? Explain how you found your answer.

Solution :

Wayne's house in the above picture is made up of using two shapes. One is triangle and and other one is rectangle.

By finding the sum of areas of triangle and rectangle, we can get the required area that will be painted.

Required area = area of triangle + area of rectangle

= (1/2 ) x b x h + l x w

=  (1/2) x 12 x 8 + (25 x 12)

=  6 x 8 + 300

=  48 + 300 = 348 square ft

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