Question

trapezoid 5a
recall that the area of a triangle is given by the equation ( a = \frac{bh}{2} ). if the area of the triangle shown is 40 ( u^2 ), determine the value of ( m ).
(there is also some other text and handwritten calculations on the page, but the main problem is about the triangle area to find ( m ))

Explanation:

Step1: Identify base and height

Base \( b = 8 \), height \( h = m + 5 \), area \( A = 40 \)

Step2: Apply triangle area formula

Substitute into \( A = \frac{1}{2}bh \): \( 40 = \frac{1}{2}(8)(m + 5) \)

Step3: Simplify the equation

Calculate \( \frac{1}{2} \times 8 = 4 \), so \( 40 = 4(m + 5) \)

Step4: Solve for \( m + 5 \)

Divide both sides by 4: \( m + 5 = 10 \)

Step5: Find \( m \)

Subtract 5: \( m = 10 - 5 = 5 \)

Answer:

5