Question

What is the length of HG?

Answer 1

Answer:

$HG = 5$

Step-by-step explanation:

Given

$HE = 8mm$

$EF = 12mm$

$Area = 68mm^2$

Find the length of HG

First, it should be noted that the displayed figure is a trapezium

The area of a trapezium is calculated by multiplying the sum of parallel sides by half its height;

In this case;

$Area = \frac{HG + EF}{2} * HE$

Substitute the values of Area, HE and EF

$68 = \frac{HG + 12}{2} * 8$

$68 = (HG + 12) * 4$

Divide both sides by 4

$\frac{68}{4} = \frac{(HG + 12) * 4}{4}$

$17 = HG + 12$

Subtract 12 from both sides

$17 - 12 = HG + 12 - 12$

$5 = HG$

$HG = 5$

Hence, the length of HG is 5mm