Question

A trapezoid was broken into two congruent triangles and a rectangle. A trapezoid is broken into 2 triangles and 1 rectangle. The triangles both have a base of 3 centimeters and a height of 12 centimeters. The rectangle has a height of 12 centimeters and a width of 14 centimeters. What is the base length, b, of one of the triangles? 3 cm 4 cm 6 cm 7 cm

Answer 1

complete question:

The picture below is the complete question.

Answer:

base of the triangles = 3 cm

Step-by-step explanation:

The trapezoid was broken into 2 congruent triangles and a rectangle. The 2 triangle have a height of 12 cm . The rectangle has a height of 12 cm and width of 14 cm .

The base length of the triangle can be computed as follows.

Note a congruent triangle have exactly the same three sides and exactly the same three angles.

area of a triangle = 1/2 × base × height

From the area of the trapezoid one can calculate the sides of the triangle.

area of the trapezoid = 1/2 × (a + b)h

where

a = top side

b = base side

h = height

area of the trapezoid = 1/2 × (a + b)h

area of the trapezoid = 1/2 × (14 + 20)12

area of the trapezoid = 1/2 × 34 × 12

area of the trapezoid = 34 × 6

area of the trapezoid = 204 cm²

204 = area of the triangles + area of the rectangle

204 =2 (1/2bh) + lw

where

b = base of triangle

h = height of triangle

l = length of rectangle

w = width of rectangle

204 = bh + (14 × 12)

204 = 12b + 168

12b = 204 - 168

12b = 36

divide both sides by 12

b = 36/12

b = 3 cm

base of the triangles = 3 cm